Were the Valar more merciful to Sauron than to Fëanor?
Even considering Sauron's skill in guile, they gave him a "second chance", didn't they? Fëanor had sworn the most terrible of all oaths and was responsible for the most terrible crimes. He defied every living thing to hinder him — even the gods. But the one thing that I grant him is that there was no deception or guile about him in his arrogance.
They didn't really give Sauron a second chance, though it might have turned out that way. The issue was Eonwë, at the the end of the War of Wrath had no right to judge his fellow Ainur. So he told Sauron, if he truly repented (which he seemed to, if only very briefly), he had to return to Valinor and be judged there. He feared the consequences of that judgement though and escaped, remaining quiet for quite a while.
When Thangorodrim was broken and Morgoth overthrown, Sauron put on his fair hue again and did obeisance to Eonwë, the herald of Manwë, and abjured all his evil deeds. And some hold that this was not at first falsely done, but that Sauron in truth repented, if only out of fear, being dismayed by the fall of Morgoth and the great wrath of the Lords of the West. But it was not within the power of Eonwë to pardon those of his own order, and he commanded Sauron to return to Aman and there receive the judgement of Manwë. Then Sauron was ashamed, and he was unwilling to return in humiliation and to receive from the Valar a sentence, it might be, of long servitude in proof of his good faith; for under Morgoth his power had been great. Therefore when Eonwë departed he hid himself in Middle-earth; and he fell back into evil, for the bonds Morgoth had laid upon him were very strong.
The Silmarillion - "Of the Rings of Power and the Third Age"
This is a very interesting question, and I thought that @suchiuomizu's answer was quite good and upvoted it. But I think it's incomplete. There are two other points which need to be considered:
First, the Valar (and Maiar) were not at all Godlike in their judgment. They made numerous mistakes, generally mistakes of being too trusting — see the question Why did Manwë not understand the concept of Evil? for a discussion of this. Bottom line: Naivety and bad judgment.
But secondly, oaths were taken very, very seriously in this world. (This is a reflection of the seriousness of oaths in the North in our own world.) Fëanor swore an oath to do evil and made it in an unbreakable form:
Then Fëanor swore a terrible oath. His seven sons leapt straightway to his side and took the selfsame vow together, and red as blood shone their drawn swords in the glare of the torches. They swore an oath which none shall break, and none should take, by the name even of Ilúvatar, calling the Everlasting Dark upon them if they kept it not; and Manwë they named in witness, and Varda, and the hallowed mountain of Taniquetil, vowing to pursue with vengeance and hatred to the ends of the World Vala, Demon, Elf or Man as yet unborn, or any creature, great or small, good or evil, that time should bring forth unto the end of days, whoso should hold or take or keep a Silmaril from their possession.
Thus spoke Maedhros and Maglor and Celegorm, Curufin and Caranthir, Amrod and Amras, princes of the Noldor; and many quailed to hear the dread words. For so sworn, good or evil, an oath may not be broken, and it shall pursue oathkeeper and oathbreaker to the world's end.
Some of Fëanor's sons later sought a way out, but failed:
Yet Maglor still held back, saying 'If Manwë and Varda themselves deny the fulfilment of an oath to which we named them in witness, is it not made void?'
And Maedhros answered 'But how shall our voices reach to Ilúvatar beyond the Circles of the World? And by Ilúvatar we swore in our madness, and called the Everlasting Darkness upon us, if we kept not our word. Who shall release us?'
'If none can release us,' said Maglor, 'then indeed the Everlasting Darkness shall be our lot, whether we keep our oath or break it; but less evil shall we do in the breaking.'
In the end, Maglor wanted to break the oath, and rightly judged that even by the standards of his world that would be the less evil, but he still didn't break it.
Yet he yielded at last to the will of Maedhros, and they took counsel together how they should lay hands on the Silmarils. And they disguised themselves, and came in the night to the camp of Eönwe, and crept into the place where the Silmarils were guarded; and they slew the guards, and laid hands on the jewels.
I think today we look at as pretty silly that someone would swear an oath to God to do evil and think that God would bind them to do that evil. But in the context of the Norse and Middle-earth, this was solemn and terrible and resolvable only by the direct intervention of Ilúvatar.
So on the one hand, the Valar had Fëanor (and sons) who were sworn to do evil and had ample proof that they took the oath seriously and would carry it out no matter what forgiveness was forthcoming from the Valar. How could they let them run loose?
On the other hand, they had Sauron and had been running in bad company but who had not made an unbreakable commitment to doing evil. That they could pardon.
In some respects they were right. Sauron was not dedicated to doing evil so much as selfish. Given his "fair hue" it was not unreasonable to think that he could be turned back to good pursuits.
Fëanor died after entering Beleriand, and (as all dead elves do) went to the Halls of Mandos. Unlike other elves (Glorfindel, for example), Fëanor never left. I don't believe we know more than that about his fate. Given that, it's impossible to tell how merciful anyone was to Fëanor. Is he still in the Halls voluntarily or involuntarily? Is he better off there or outside?
I personally don't see them be particularly merciful to any of the two wrongdoers. Both times, the Valar just step away, let the prideful choose their own path, seal their own fates and suffer the consequences of their own mistakes. And then just sometimes send some Maiar to clean up after the most extreme outbursts of evil.
Sauron is the maker of his own second chances. And the third, and so on. While Morgoth's evil deeds where well known by the end of the First Age, Sauron could still get away with "I just chose a side and followed orders", and he did. He then spent two Ages trying to usurp power over Middle-earth, building himself a base and an army, plotting and corrupting, attempting to control everything magically.
Fëanor didn't. He just rode into every fight he could find and after meeting first serious opposition, got himself killed. But that's hardly Valar's doing. He chose differently from Sauron, that's all.
No one from major Arda sapient races dies completely, there's life after death. Ainur and Elves don't even die irreversibly. For them, dying means losing what you had, losing ability to affect the world, forceful relocation to remote places, but not destruction. Unlike Men, all of them can come back. Both Sauron and Fëanor can.
In some drafts, there are prophecies about the return. For example, in History of Middle-earth v.4 "The Shaping of Middle-earth", chapter 3 "Quenta" (early version of "Quenta Silmarillion" from 1930s) contains the following:
Thus spake the prophecy of Mandos, which he declared in Valmar at the judgement of the Gods, and the rumour of it was whispered among all the Elves of the West: when the world is old and the Powers grow weary, then Morgoth shall come back through the Door out of the Timeless Night; and he shall destroy the Sun and the Moon, but Eärendel shall come upon him as a white flame and drive him from the airs. Then shall the last battle be gathered on the fields of Valinor. [...]
Thereafter shall the Silmarils be recovered out of sea and earth and air; for Eärendel shall descend and yield up that flame that he hath had in keeping. Then Fëanor shall bear the Three and yield them unto Yavanna Palúrien; and she will break them and with their fire rekindle the Two Trees, and a great light shall come forth; and the Mountains of Valinor shall be levelled, so that the light goes out all over the world.
The Shaping of Middle-earth, "The Quenta," section 19
So in principle, nothing is completely lost for both characters. One day thay may act again. If it hasn't happened yet, it means their time hasn't yet come. And Valar didn't do anything particular to stop either of them from having one more go at it.
In addition to the oaths that Fëanor swore, there was also the killing of the Teleri when they would not surrender their ships. Kinslaying is frowned upon.
