Two reasons I book rev tickets online:
1) Get to use the 10% discount code.
2) 1000 bonus miles.
So the answer to your question is that it really depends on what you're booking. Awards are definetly handled better with an agent, and in that case since you're getting no miles anyway, you might as well do it over the phone. I always do rev tickets online unless there's a huge routing and I need a human being. In that case I call the web desk.
[This message has been edited by bpauker (edited 10-24-2002).]