Typically and historically:
Rails is an all-in-one solution and is quite opinionated (though it is getting better as the Rails team break it apart a bit more each release) and if you do things the Rails way you'll have a good time and you'll benefit from its developer productivity enhancements.
Sinatra, on the other hand, is much more lightweight from the start and its focus is much narrower than rails, which means if you want all the features that Rails has you'll have a bit of work to do (and you may as well use Rails at that point anyway to benefit from the integration between its various features).
However:
It's not quite so cut and dry any more since the Rails team have put an awful lot of effort into separating Rails into _optional_ components and ultimately giving you the same sort of flexibility as Sinatra (I believe a lot of the separation in Rails ~3 was inspired by Sinatra and other similar lightweight web frameworks)
So these days it comes down to whether you start with Rails and cut it down to give you only what you need, or start with Sinatra and build on it - and this is the point at which your decisions come.
For example if I were to create a micro service or an API only application I probably wouldn't use Rails, I'd likely use Sinatra (actually I probably wouldn't use Ruby at all these days, but that's a different story!). However if I were to create a full web application with front end and all (assuming HTML generated by backend in this case), then I'd probably consider Rails over Sinatra because it comes with all the bells and whistles I will (and might) need.
I hope that helps some. Essentially it boils down to what you're creating, but personally I wouldn't reach for Rails as the de facto any more.