We use dropwizard only for rest APIs currently. Our HTML and JS are served up with an in-house framework that has plugins for less, minimization, svg inlining, etc. We have open tasks to both publish it and make it hostable in dropwizard directly.
We use it for both REST APIs on top our services and rendering templated HTML. We had to bastardize the asset bundle extension considerably for that though. Once we got things working we didn't want to go back.