In The Hobbit: An Unexpected Journey movie, Gandalf appears particularly subdued/submissive in Saruman's presence during their meeting at Rivendell. Why is this so? Is it simply because Saruman is of the White, while Gandalf is a Grey or does he already suspect that something's amiss and purposely appears so. Subsequent dialogue sees Saruman rebuking Gandalf for trying to sneak around and do things without his knowledge.
I'm not so sure the behaviour you interpret as being submissive (or subservient is probably a better term) is actually that at all. Gandalf seems more sheepish to me at being caught assisting a bunch of Dwarves and a Hobbit in some weird and wonderful adventure that Saruman neither knows about nor approves of.
Saruman, being head of the White Council, perhaps doesn't feel that a fellow member of the White Council should be wasting his time with such trivial things.
I also think there's an element of Saruman imposing his authority as the supposed Head of the White Council, particularly when Galadriel had preferred Gandalf be given that role.
Tolkien also stated that Saruman knew that Gandalf possessed the greater power and wisdom and disliked him for it.
Saruman the White was the chief Istari; That I think would refer to Gandalf's Order which he clearly stated himself that Saruman was leader of, also the fact that Gandalf was made the White after Saruman's betrayal (The White Wizard status must have been superior to the grey.) I believe there was jealousy from the very start of when the Istari came to Middle Earth, Saruman jealous of Gandalf being gifted an elvish ring as to Saruman getting one. Then the fact that Galadriel wanted Gandalf to be head of the white council (Saruman's Position in the White Council) lead to Saruman holding a future grudge - more hate against Gandalf and now Galadriel.
I always liked Saruman better than Gandalf, so I probably am being slightly biased. But I always thought that Gandalf was little fearful of Saruman. He seems to have a lot of respect for Saruman when Saruman treats him terribly.
Saruman was the head of the Istari, Gandalf's ascension to the white was after his fight with the Balrog; after Saruman had been exposed as working with Sauron. At the time of the Hobbit, Gandalf is aware that a ring of power is involved but not which, and Saruman is still pretending that this is all paranoia on Gandalf's part. The Istari are outside of the normal run of things. Check the Silmarillion for a fuller understanding.
As has been mentioned, Saruman was both head of the Order of Istari(wizards) and head of the Council of the Wise(also known as 'the White Council').
Plus, this is in Medieval times, so formality and manners were tighter and accepted more widespread than nowadays. Even when Gandalf arrived with Thorin's Company to Rivendell and greets Elrond as 'My friend' he bows his head as he does it, as deferential respect, etc.
In the books even though Gandalf respects and acknowledges the position of Saruman he isn't as submissive towards him as you'd think. The relation between Istari are more like collegues, each appears to have different specialty (Saruman is the one more learned, he also studies arts of the enemy to counteract agaisnt them, which ultimately proves to be his downfall, also he always tried to experiment, expand his understanding of things and influence like when he dares to use palantir of Orthanc, as Gandalf says ,,Perilous to us all are the devices of an art deeper than we possess ourselves", while the Istari are Maiar in disguise it seems their full knowledge and power is dimmed, even their memory of Aman so they would focus on mission, they are forbidden from using their power to subjugate races of Middle Earth, they must act as councillors and guides to them, inspiring the inhabitants of to oppose Dark Lord themselves:
,,now their emissaries were forbidden to reveal themselves in forms of majesty, or to seek to rule the lives of Elves and Men by an open display of power. "
,,For it is said indeed that being embodied the Istari had needs to learn much anew by slow experience, and though they knew whence they came the memory of the Blessed Realm was to them a vision from afar off, for which (so long as they remained true to their mission) they yearned exceedingly. Thus by enduring of free will the pangs of exile and the deceits of Sauron they might redress the evils of that time." Unfinished Tales.
So as a full not restricted divine beings their knowledge and skill would be evidently greater maybe much greater than mortals or elves could ever achieve, but in Middle Earth they had to start anew, lessened in a way), Radagast though he was more distracted from his direct mission by fascination with animals and plants of Middle Earth (he was in origin one of the Maiaric servants of Yavanna after all) still he significantly contributed to the cause, he acted at times as a sort of a spymaster of the White Council, gathering news and passing them around for operatives :), Gandalf well his specialty is harder to place, he appears to be like a stereothypical wandering wizard, at time he acts like a councillor, court wizard for various kings, he travels around much more than Saruman and Radagast combined (though we know that at one point Saruman before setting his home in Isengard under permission of Ruling Steward of Gondor, too was wandering about the lands he even went to far East/lands of Rhun together with two Blue Wizards/Ithryn Luin but only he returned to the westlands, Saruman also spent a long time studying hoards of books and scrolls from libraries and archives of Minas Tirith) but he solves problems of those who would ask him for help, doing various plans and orchestrating their fulfillment, real strategist.
This division of labour of sorts, would definitely require the large dose of independence of them inide the Order but still retaining hierarchy, the White Council was more formal body but it was helding meetings from time to time and many of the Wise or Eldar elf-lords too had their influence there and here Saruman would have greater power residing over meetings, providing info on the discussed matters that others lacked (especially about the Rings of Power and secrets of their making that few even of elves remembered), he would be really important and so his pride would grew but it does not appear that Gandalf felt especially subjected to Saruman's will, Grey Wizard was more humble and could consider Saruman's greater knowledge superior in certain matters to frequently discuss it with him but their known conversation on the council's meeting shows that Gandalf wasn't at all daunted by Saruman or would allow him to overly control him. It is seen clearly that Gnandalf had this independent streak and certain issues cause that Saruman's jelousy towards him was constantly growing up until his full betrayal:
,,Saruman soon became jealous of Gandalf, and this rivalry turned at last to a hatred, the deeper for being concealed, and the more bitter in that Saruman knew in his heart that the Grey Wanderer had the greater strength, and the greater influence upon the dwellers in Middle-earth, even though he hid his power and desired neither fear nor reverence. Saruman did not revere him, but he grew to fear him, being ever uncertain how much Gandalf perceived of his inner mind, troubled more by his silences than by his words. So it was that openly he treated Gandalf with less respect than did others of the Wise, and was ever ready to gainsay him or to make little of his counsels; while secretly he noted and pondered all that he said, setting a watch, so far as he was able, upon all his movements.
It was in this way that Saruman came to give thought to the Halflings and the Shire, which otherwise he would have deemed beneath his notice. He had at first no thought that the interest of his rival in this people had any connexion with the great concerns of the Council, least of all with the Rings of Power, For indeed in the beginning it had no such connexion, and was due only to Gandalf's love for the Little People, unless his heart had some deep premonition beyond his waking thought. For many years he visited the Shire openly, and would speak of its people to any who would listen; and Saruman would smile, as at the idle tales of an old land-rover, but he took heed nonetheless."
,,Yet in truth Saruman's spying and great secrecy had not in the beginning any evil purpose, but was no more than a folly born of pride. Small matters, unworthy it would seem to be reported, may yet prove of great moment ere the end."
There is also a bit about their strained relations:
,,Now because of his dislike and fear, in the later days Saruman avoided Gandalf, and they seldom met, except at the assemblies of the White Council. It was at the great Council held in 2851 that the "Halflings' leaf" was first spoken of, and the matter was noted with amusement at the time, though it was afterwards remembered in a different light. The Council met in Rivendell, and Gandalf sat apart, silent, but smoking prodigiously (a thing he had never done before on such an occasion), while Saruman spoke against him, and urged that contrary to Gandalf's advice Dol Guldur should not yet be molested. Both the silence and the smoke seemed greatly to annoy Saruman, and before the Council dispersed be said to Gandalf: "When weighty matters are in debate, Mithrandir, I wonder a little that you should play with your toys of fire and smoke, while others are in earnest speech."
But Gandalf laughed, and replied: "You would not wonder if you used this herb yourself. Yon might find that smoke blown out cleared your mind of shadows within. Anyway, it gives patience, to listen to error without anger. But it is not one of my toys. It is an art of the Little People away in the West: merry and worthy folk, though not of much account, perhaps, in your high policies."
Saruman was little appeased by this answer (for he hated mockery, however gentle), and he said then coldly: "You jest, Lord Mithrandir, as is your way. I know well enough that you have become a curious explorer of the small: weeds, wild things and childish folk. Your time is your own to spend, if you have nothing worthier to do; and your friends you may make as you please. But to me the days are too dark for wanderers' tales, and I have no time for the simples of peasants."
Gandalf did not laugh again; and he did not answer, but looking keenly at Saruman he drew on his pipe and sent out a great ring of smoke with many smaller rings that followed it. Then he put up his hand, as if to grasp them, and they vanished. With that he got up and left Saruman without another word; but Saruman stood for some time silent, and his face was dark with doubt and displeasure." Unfinshed Tales
Gandalf gave quite fitting notion about Saruman's ways, but still he had trust in him:
,,I might perhaps have consulted Saruman the White, but something always held me back.’
‘Who is he?’ asked Frodo. I have never heard of him before.’
‘Maybe not,’ answered Gandalf. ‘Hobbits are, or were, no concern of his. Yet he is great among the Wise. He is the chief of my order and the head of the Council. His knowledge is deep, but his pride has grown with it, and he takes ill any meddling. The lore of the Elven-rings, great and small, is his province. He has long studied it, seeking the lost secrets of their making; but when the Rings were debated in the Council, all that he would reveal to us of his ring-lore told against my fears. So my doubt slept - but uneasily. Still I watched and I waited." Fellowship of the Ring
,,‘But at the western edge of Mirkwood the trail turned away. It wandered off southwards and passed out of the Wood-elves’ ken, and was lost. And then I made a great mistake. Yes, Frodo, and not the first; though I fear it may prove the worst. I let the matter be. I let him go; for I had much else to think of at that time, and I still trusted the lore of Saruman." Fellowhsip of the Ring "Who told you, and who sent you? " I asked.
' "Saruman the White," answered Radagast. "And he told me to say that if you feel the need, he will help; but you must seek his aid at once, or it will be too late."
'And that message brought me hope. For Saruman the White is the greatest of my order. Radagast is, of course, a worthy Wizard, a master of shapes and changes of hue; and he has much lore of herbs and beasts, and birds are especially his friends. But Saruman has long studied the arts of the Enemy himself, and thus we have often been able to forestall him. It was by the devices of Saruman that we drove him from Dol Guldur. It might be that he had found some weapons that would drive back the Nine." Fellowship of the Ring