I've seen a lot of UI frameworks starting to push unit testing down to the UI layer.
In our opinion, does testing the UI logic make sense for this layer or should you focus on E2E testing with tools like Selenium?
What I would do depends so much on the actual code base and technologies involved that it's quite difficult to say much in that direction. With that said, and generalizing a bit, I would expect to see some kind of a "pyramid" shape in place where most of the volume would be in low level, isolated unit tests for individual objects or small clusters of objects and the closer to the system's boundaries your tests would get the fewer and fewer of such tests you would have.
I don't know much at all about Vaadin (even though it's built by a bunch of Finns – we're not that small a country ) and I've only been exposed to GWT on one project shortly. It does seem, however, that most web frameworks aren't really all that test-friendly. They might go really far in making integration testing straightforward but at the same time they might make it really difficult to isolate individual objects for unit testing.
There's a guy in Norway called Johannes Brodwall who's been promoting raw Servlets the past couple of years. It may sound like going back to the stone age but he's got a point – web frameworks can very easily become like an octopus that spreads its tentacles throughout your code base. Anyway, I sense that this is going towards an unnecessary (and somewhat off-topic) rant so I'll just stop here...