This answer necessarily includes spoilers from The Force Awakens and The Last Jedi, as well as the original trilogy. Spoiler tags have not been used, as discussing these spoilers is the entirety of the answer, so be warned.
The First Order doesn’t have nearly the power of the Empire
As fantastic as Null’s answer is, I feel there is a fundamental flaw in the very question asked: the premise that the First Order is stronger than the Empire. Starkiller may have been (dramatically) more powerful than the Death Star, but the First Order seemed to be banking everything on it while the Death Star was just another toy for the Empire. The victory in Return of the Jedi would have been no greater than the victory in A New Hope (destruction of a Death Star) had not both the Emperor himself and Darth Vader been on board the Death Star at the time of its destruction. That was the real victory.
But aside from that, as The Force Awakens begins, the Resistance operates openly, no longer hiding in shadows. They have major operations, territory of their own. The New Republic, too, controlled a lot of territory, and while its control over the galaxy was tenuous, it did seem to be seen, outside the First Order itself, as legitimate.
On the other hand, the First Order does not control the system, as the Empire did. It controls limited territory, and it has limited resources and manpower. Under the Empire, personnel were uncountable, endlessly replaceable. Darth Vader could and did kill subordinates left and right just to send a message—and that message was heard loud and clear. Anyone and everyone could and would be replaced. There was no indication that this policy was ever to the Empire’s detriment, at least in terms of reliably manning various positions.1 Stormtroopers and TIE pilots were absolutely loyal without any particular effort on the Empire’s part.
Compare this to what we see in The Force Awakens. Failures and insubordination have to be handled carefully. Stormtroopers have to be carefully monitored, and their ranks have to be filled through a kidnapping program. Hux is portrayed as fairly capable, but unduly arrogant and self-assured, and his ego would be suicidal in the Empire, as would his failure to back up his claims. Neither he nor Captain Phasma would have survived Finn’s defection if Kylo Ren was Darth Vader—and if the First Order was the Empire, and could afford to do that. But the First Order is not the Empire, and Snoke and Kylo Ren know it—and Kylo Ren is not Darth Vader, and Snoke and Kylo Ren know that too. They know that they need Hux, they cannot easily replace him. Indeed, Snoke seems to be willing to put up with quite a lot of incompetence on the part of his apprentice Ren, which is telling in itself.
Finally, we have the speech on Starkiller itself. No one in the Empire was giving the troops inspirational speeches. The troops were going to fight, and die if necessary, because the Empire could and would force them to do so. That rally would have been completely out of place in the Empire.
So between Episode VI and VII, the First Order has been putting on a strong face, because strength is their draw, but at least part of it is a bluff. They have considerable resources, obviously, but they do not have limitless resources—and the Empire very nearly did.
However, when The Last Jedi starts, we see that banking everything on Starkiller—even though it only got used once—appears to have paid off for the First Order. Even though the Resistance destroyed it in short order, that initial volley massively improves the First Order’s position in the galaxy and leads to the Resistance’s desperate straits that we see at the beginning of The Last Jedi, as well as the reluctance of the Resistance’s supposed allies to actually come to their aid. In yet another parallel to A New Hope, it seems that the victory that ended The Force Awakens has not won the war for the Resistance—like the Rebellion before it, which faced an existential threat in the form of the Death Star, the Resistance absolutely had to destroy the Starkiller or it would have been destroyed. But destroying the Starkiller doesn’t destroy the First Order, just as destroying the Death Star did not end the Empire.
But even so, the Empire’s position in the original trilogy, right up until the point where the Emperor and Darth Vader die on the Death Star, is vastly superior to the First Order’s. The fleet chasing the Resistance cruiser for most of the movie seems to be most of the First Order as it exists at the time—no additional ships are available to change the dynamic, at least none close enough to intervene before the cruiser runs out of fuel anyway. Poe Dameron implies that the dreadnought that gets destroyed is not the only one that the First Order has, nor does the leadership of the First Order react terribly strongly to its loss, but nonetheless it is very difficult to imagine Palpatine and Vader standing on the bridge of a star destroyer for hours waiting for the cruiser to run out of fuel. The assault on Crait paled in comparison to the size of the attack on Hoth—and the Resistance’s defense was even more paltry, in comparison to the Rebellion’s defense of Hoth.
One can even begin to suspect that Kylo Ren is right—the days of both Empire and Rebellion are over, and the First Order and Resistant seem to be mere remnants that refuse to give up the ghost. It would be rather interesting for Episode IX to show a galaxy moving on without either of them, though that almost-certainly won’t actually happen. I hope, at least, that the leadership of both First Order and Resistance are shown having to reorient themselves to a galaxy bigger than either of them.
- The Empire’s behavior with respect to its personnel was definitely inefficient, in that motivated and loyal people just do better work, and its callous attitude towards life was no doubt a major recruiting tool for the Rebellion. I am not defending the Empire’s behavior as ideal. What I am saying is that Vader never needed to worry about there not being a replacement for anyone and everyone around him. He could kill them without a second thought if he wanted, and not only would he not get called on it, it also would not interfere with the Empire’s operations. So yes, the Empire’s behavior was inefficient—but to all appearances, they could afford it.