I've been lucky enough never to have a V1 cut in an actual airplane, but if the sims are to be believed, the amount of rudder necessary to keep the airplane on the runway is "most of it", whether you're in a Beechjet or a 747. There's some variation, obviously, but *at or around v1*, they're all pretty similar, AFAICT. Presumably because whatever the amount of rudder authority which is necessary is mandated by certification standards, and there's an obvious countervailing interest in keeping the rudder/stab as small as possible for efficiency purposes. Thus, "most of it", QED, etc etc.
Where things get interesting is at lower speed. In a tail-engine bizjet, it's presumably not a huge big deal if you lose one at low speed, certainly I don't remember ever having trained for it. In a 74, on the other hand, losing one (outboard) engine right after you've spooled all the way up is (reportedly) Mr. Toad's Wild Ride.