There are pro’s and cons to both. However, for most athletes, push ups are way too easy and you need to do other versions to keep it interesting and progressive. Try one arm pushups (keeping your back flat at all times and your arm close to your body). When you can do that with ease, do one arm one leg pushups. Hold one leg up while you do one arm pushups. Great exercise that rock the core.
When that gets easy, try tiger bend pushups in which your elbows touch the floor like a reverse skull crusher. When you can do tiger bend pushups with one arm, you are a serious bad ass.
After that, try Handstand pushups against a wall and work on doing them free standing. Great drill for taking your overhead pressing through the roof. Also try them on stools to increase the range of motion. Great exercise and great party trick.
Mike Mahler