The future Sentinels in X-Men Days Of Future Past are clearly shown adapting to powers thrown at them by copying them. Isn't that what Rogue's DNA would allow for, not Mystique's? Mystique can just change appearance, not copy powers ... right? So why would study of her mutant genes allow for the abilities of the future Sentinels?
As far as has been shown, yes, that is correct. At least, mostly.
There were two massive improvements shown:
The second ability is pretty evidently derived from Mystique's abilities. The power set change ups aren't definitively being copied or added on the fly. Remember, by this point, the Sentinels have been hunting mutants for a very long time. It is entirely conceivable (and even likely) that Trask Industries has been adding to the Sentinel's capabilities and weapon sets over time - giving them the necessary abilities to handle the mutants they come up against.
But without Mystique's abilities giving the Sentinels the abilities to reshape themselves, they wouldn't be able to stand up to the mutants as well.
We can't forget that Trask was legitimately a genius. Mystique's DNA was instrumental in allowing the Sentinels to adapt, but he certainly didn't just copy and paste that one trick and call it done. Odds are he saw something within the function of Mystique's ability that jogged his imagination, and then his own genius (and that of other researchers after his death) allowed them to go from "changing appearance" to "changing ability."
Think of it like the old story of Newton watching the apple fall from the tree: what he witnessed (i.e. an object falling due to gravity) simply gave him the spark to eventually describe the patterns of not only gravity, but inertia and a number of other laws governing the motion of objects in general.
Mystique's ability gave Trask a mechanism for rapid physical change. The nature of those changes, and the abilities available to the Sentinels from then on, was no doubt the result of further study and decades of refinement.