Constant motion is a must. Sorry (American) Football, Tennis, Baseball. Also, I have to rule out track and field and swimming, if you are talking about the distance part absolutely, but sprinting sorry but no. Soccer (Football for the rest of you), Rugby, Wrestling, MMA, etc. They all are very physically demanding and have very, very few breaks. However, contact is an absolute must. Sorry Soccer, you are gone, along with XC, and other distance sports. To me it comes down to these choices. Boxing, Wrestling, Rugby, MMA. Wrestling is out, MMA beats it with sheer brutallity. However, Boxing and MMA lack the pure time factor of Rugby. I've boxed and played rugby. I've never been in an MMA fight, (thank god, gotta protect the moneymaker *motions towards face*) but honestly it suffers from the same mistake boxing does. Sure you're are beat to all holy hell by the end (in even fights), but after a good boxing match, you're done for a while. Sure you train, you spar, you run. But I think Rugby takes the cake, full body contact with large masses, no padding, virtually constant motion, and a much longer period of time that you are moving.
All in all, I have boxed and played rugby. From personal experience I can say that I've been sore as all holy hell after boxing bouts. However, I don't want to move after I play rugby. The game is physically demanding and brutal. It's not about being sore afterwards, it's about being exhausted.
TLDR: Rugby.