Upload & Sell: Off
"Top of press box in stadium"
Like top of the bleachers, top of the press box?
From that distance, there is not a whole lot of AF going on! If the lighting is decent and/or ISO capable, set the DSLR to manual focus with the expected f/stop to get the field in focus and proper ISO to maintain exposure. (remember that video exposure is usually 1/60th, so it's a pretty generous exposure to allow for lower ISO and higher DOF.)
Otherwise, I think the main factor in buying is what you're trying to convince yourself of? Do you want a DSLR or a video camera. Do you have other purposes for either? IMO, both will work, with the DSLR being more versatile for the photo end.
However, if you want closeups - as others have mentioned, most DSLR's will not be up to the task of AF'ing with sports action (I don't know about the new 70D's capabilities)