If you compare the "Getting Started" sections for both frameworks (Dropwizard's is here: http://www.dropwizard.io/0.9.1/docs/getting-started.html), it looks like the initial setup for Apollo is a lot less complex. This may be a significant advantage, because it cuts down project setup time, which is one of the annoying parts of microservices.
However, I can imagine having to pay for this once you need some more advanced features. Dropwizard comes with a lot of stuff for configuration management and integration, which I guess is mostly missing in Apollo.