I should prefer the one with accuracy. It justs fits me better. Obviously, by the word 'should', I don't, although I think it might just be that I enjoy the tactics of American Football from the example, and it is the only sport I will choose to watch. Ultimately though the sports I enjoy playing from time to time (read; when forced to do sports) usually involve a racket/bat/club etc which fall into the prescision category, so I guess I can still go with accuracy without being too much of a hypocrit.
A violent sport for the sake of violence isn't something I'd do. If it's a sport that happens to be one in which violence/brute force is a necessary part, as long as I am competant at the game and happen to enjoy it, than yea I'd probably be playing it if the opportunity to do so was present.
As far as american football vs tennis. Both require accuracy - the football QB has to throw accurately to get the ball to the teammate down the field, a tennis player has to hit the ball accurately and get it to go where it needs to in order to score the point.
Personally, I'd rather play Am. football than tennis, because I'm better at and enjoy the former more than the latter.
It really depends. I tend to only like a few sports which would be: volleyball, tennis, swimming and rugby. Anything else is boring to me. So it isn't a factor of whether it is violent or not, it's what catches my attention.