It really depends where you are weak in the movement. When you fail a max effort attempt, where in the movement do you fail?
Everyone will benefit from floor press because of the emphasis on the triceps in proper bench press technique. But if lockout is your weakness, as it is for many people, floor press is one of the best exercises you can do for it. Because of the limited range of motion, you will be able to really focus on developing your triceps and the lockout of the bench.
So the floor press is one of the best assistance exercises you can do for the bench. And for the crossfitter, the floor press will also have benefit for your overhead press.
Also, if you want more information, you can check out Louie Simmons articles on http://www.westside-barbell.com
(wfs) or http://www.elitefts.com