I once bought a couple of books that explained many different trapping methods among them were snares and deadfalls. I, like you, pondered the same question and decided to try snares first. Never got around to the deadfalls cause the snares work so well.
For the life of me I couldn't figure how to fine tune a deadfall so it would stay suspended through wind and weather and still be sensitive enough to be set off by a little critter like a rabbit.
My best advice:
try snares.