JAX-RS is really nice for building APIs and I actually prefer the way it works to Sinatra, especially if using it with Groovy.
But, this isn't Sinatra vs EE6, its Rails vs EE6, so its not a proper comparison.
To compare with Rails you've got to look at other parts of EE6: JSF + CDI + JPA, which is an awful mess. JSF by itself is enough to kill its usability for many modern applications, the amount of state JSF carries around is ridiculous.