I think it's a real question of taste between both Sinatra and Ramaze. Both good, both light.
The big difference would be that Ramaze is more MVC. Sinatra in the other hand works like a DSL and is RESTful.
I would suggest that you read the GET_STARTED of them which wouldn't take more than a couple of minutes, and you'll see what the difference is.
I personaly like them both (with a preference for Ramaze), but one thing that could help you make a decision is the fact that Sinatra is little bit more popular (i think), so you may find more docs on the web.
In the other hand, you can use Ramaze and help making it more popular. The IRC channel for Ramaze is full of people (including me) who will be happy to help you and answer all your questions.
Hope it helps. Mig