Are pushups on elevated dumbbell handles better than flat handed pushups due to greater range of motion?
This is my opinion based on studying muscle movement, perhaps some may not agree.
Range of motion is often misunderstood. Your weakest FUNCTIONAL strength is when the muscles are at 90 degrees with each other. That is why when you do the ass to ground squat, you cannot carry the same load as the horizontal thigh one. And again that is why you can carry a heavier load in the deadlift. Just a matter of angles.
In the case of the push up, just get to the correct angle. The range of motion is immaterial. When you have reached a certain level, then you can do the bench press for further improvement. What you want is to workout with the heaviest load you can with the set number of reps for maximum gain.
If you have the chance, do a 1 max weighted squat as described above and observe for yourself. The lower you go, the less weight you can carry on the way up.