This is based purely on the movies; I have never read or watched any supplemental material.
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, 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.
The First Order puts 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.
- 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.