It is pretty much personal preference, as Bob said.

I like the arrow flight and somewhat improved accuracy I get with an elevated rest - on recurves. Elevated rests aren't aesthetically pleasing on a longbow. The other side of the coin is elevated rests can break at the worst time, so shooting off the shelf is one less potential problem.

So, I do both. For shooting targets and keeping score, I use a rest. For hunting and generally goofing off with a bow, I shoot off the shelf.