Rails is a Rack app too. While I agree there are diminishing returns the lower in the stack you go, your original reduction is misleading.
The choice between Sinatra and Rails can reasonably be debated, but there's little reason to write a JSON API in Rack unless you need control of protocol details that neither abstraction provides. Sinatra/Rails are frameworks, Rack is middleware.
The choice between Sinatra and Rails can reasonably be debated, but there's little reason to write a JSON API in Rack unless you need control of protocol details that neither abstraction provides. Sinatra/Rails are frameworks, Rack is middleware.