Thanks for the mention! (I'm the webapp2 author).

A big advantage of webapp2 is that you can use existing (and probably future) SDK libraries without adaptation. Many App Engine services (blobstore, mail handler, deferred etc) use handlers made for webapp. With webapp2 you get all those handlers working out of the box with extra benefits: webapp2 is a lot easier to extend and includes the most glaring webapp missing features.

Also, you can use all the examples from the App Engine documentation with it, since it is made to be compatible with webapp. And later you learn the new, extended features.

I'll second this suggestion. In my experience so far, webapp2 is a great way to get beyond some of the stranger idiosyncrasies of the default webapp without being overwhelmed or completely throwing away the benefits of Google's extensive documentation. If you like an extension or modified feature, use it. If not, do the way Google tells you to and it'll work just fine.

If you use nothing else, the extended routing functionality and lazy loading of handlers are big improvements and are pretty painless to implement.