Have you read their documentation?
They serve two very different purposes. Dojo is a complete JavaScript client-side framework. IMO it has a fairly steep learning curve, is very functional, and due to non-technical reasons did not become one of the dominant players in the JavaScript framework arena.
DWR began as a way to mask the differences between server-side
Java and client-slide JavaScript (and that's all I've used it for, so
you should read up on it). It makes client-side JavaScript Ajax calls look like calls to native Java objects. It's pretty cool, and I've used it very effectively in that role.
None of these are Struts questions, however. If you have further questions regarding non-Struts, client-side frameworks you should ask them in the appropriate forum.