What sets them apart from other box rifles? Everything's already been covered, but below are the reasons I've been using and recommending tikkas above all the other options. And I've put them in rough order of importance to me:
Action - smoother than anything I've tried, and more reliable, I've never had any feeding, extraction, ejection, or other issues, can't stand that happening with hunting rifles, they're supposed to work, every time
Trigger - crisp and light out of the box, simple turn of a screw puts them at ~2lbs
Scope mounting - I like the warne and sportsmatch rings, clamp directly to the receiver, it's solid, and simple
Stock - ergonomic enough, stiffer than most, bedding is pretty optional, unlike most
Accuracy - I've had one tikka before that didn't shoot very well, other than that, all the others are more consistently accurate than most other rifles I've had to tweak to be accurate, and that's straight out of the box