Ok, my bad, was reading too fast. Halcyon seems nice, really focus on JSON, which can be handy when building a REST/JSON API. The answer will be more a personal choice, within what you prefer. Sinatra has a way to describe routes and endpoints using its DSL that, in my opinion, is way nicer for a simple REST API that Halcyon. Halcyon looks a lot more like Rails (in routing, controllers etc)., which might not always ease readibility.

Still, there's no real good answer here. Padrino/Halcyon can both work on Rack, Thin or Mongrel, so performance would normally be almost the same. The difference will be in the style of code you want to write: simple and really explicit DSL like Sinatra/Padrino, or something more like Rails with Halcyon.