Currently Google App Engine supports both Python & Java. Java support is less mature. However, Java seems to have a longer list of libraries and especially support for J
One think to take into account are the frameworks you intend yo use. Not all frameworks on Java side are well suited for applications running on App Engine, which is somewhat different than traditional Java app servers.
One thing to consider is the application startup time. With traditional Java web apps you don't really need to think about this. The application starts and then it just runs. Doesn't really matter if the startup takes 5 seconds or couple of minutes. With App Engine you might end up in a situation where the application is only started when a request comes in. This means the user is waiting while your application boots up. New GAE features like reserved instances help here, but check first.
Another thing are the different limitations GAE psoes on Java. Not all frameworks are happy with the limitations on what classes you can use or the fact that threads are not allowed or that you can't access local filesystem. These issues are probably easy to find out by just googling about GAE compatibility.
I've also seen some people complaining about issues with session size on modern UI frameworks (Wicket, namely). In general these frameworks tend to do certain trade-offs in order to make development fun, fast and easy. Sometimes this may lead to conflicts with the App Engine limitations.
I initially started developing working on GAE with Java, but then switched to Python because of these reasons. My personal feeling is that Python is a better choice for App Engine development. I think Java is more "at home" for example on Amazon's Elastic Beanstalk.
BUT with App Engine things are changing very rapidly. GAE is changing itself and as it becomes more popular, the frameworks are also changing to work around its limitations.
Based on how much I hear Java people complain about AppEngine compared to Python users, I would say Python is much less stressful to use.
Gone with Python even though GWT seems a perfect match for the kind of an app I'm developing. JPA is pretty messed up on GAE (e.g. no @Embeddable and other obscure non-documented limitations). Having spent a week, I can tell that Java just doesn't feel right on GAE at the moment.
I'm biased (being a Python expert but pretty rusty in Java) but I think the Python runtime of GAE is currently more advanced and better developed than the Java runtime -- the former has had one extra year to develop and mature, after all.
How things will proceed going forward is of course hard to predict -- demand is probably stronger on the Java side (especially since it's not just about Java, but other languages perched on top of the JVM too, so it's THE way to run e.g. PHP or Ruby code on App Engine); the Python App Engine team however does have the advantage of having on board Guido van Rossum, the inventor of Python and an amazingly strong engineer.
In terms of flexibility, the Java engine, as already mentioned, does offer the possibility of running JVM bytecode made by different languages, not just Java -- if you're in a multi-language shop that's a pretty large positive. Vice versa, if you loathe Javascript but must execute some code in the user's browser, Java's GWT (generating the Javascript for you from your Java-level coding) is far richer and more advanced than Python-side alternatives (in practice, if you choose Python, you'll be writing some JS yourself for this purpose, while if you choose Java GWT is a usable alternative if you loathe writing JS).
In terms of libraries it's pretty much a wash -- the JVM is restricted enough (no threads, no custom class loaders, no JNI, no relational DB) to hamper the simple reuse of existing Java libraries as much, or more, than existing Python libraries are similarly hampered by the similar restrictions on the Python runtime.
In terms of performance, I think it's a wash, though you should benchmark on tasks of your own -- don't rely on the performance of highly optimized JIT-based JVM implementations discounting their large startup times and memory footprints, because the app engine environment is very different (startup costs will be paid often, as instances of your app are started, stopped, moved to different hosts, etc, all trasparently to you -- such events are typically much cheaper with Python runtime environments than with JVMs).
The XPath/XSLT situation (to be euphemistic...) is not exactly perfect on either side, sigh, though I think it may be a tad less bad in the JVM (where, apparently, substantial subsets of Saxon can be made to run, with some care). I think it's worth opening issues on the Appengine Issues page with XPath and XSLT in their titles -- right now there are only issues asking for specific libraries, and that's myopic: I don't really care HOW a good XPath/XSLT is implemented, for Python and/or for Java, as long as I get to use it. (Specific libraries may ease migration of existing code, but that's less important than being able to perform such tasks as "rapidly apply XSLT transformation" in SOME way!-). I know I'd star such an issue if well phrased (especially in a language-independent way).
Last but not least: remember that you can have different version of your app (using the same datastore) some of which are implemented with the Python runtime, some with the Java runtime, and you can access versions that differ from the "default/active" one with explicit URLs. So you could have both Python and Java code (in different versions of your app) use and modify the same data store, granting you even more flexibility (though only one will have the "nice" URL such as foobar.appspot.com -- which is probably important only for access by interactive users on browsers, I imagine;-).
June 2013: This video is a very good answer by a google engineer:
http://www.youtube.com/watch?v=tLriM2krw2E
TLDR; is:
I've been amazed at how clean, straightforward, and problem free the Python/Django SDK is. However I started running into situations where I needed to start doing more JavaScript and thought I might want to take advantage of the GWT and other Java utilities. I've gotten just half way through the GAE Java tutorial, and have had one problem after another: Eclipse configuration issues, JRE versionitis, the mind-numbing complexity of Java, and a confusing and possibly broken tutorial. Checking out this site and others linked from here clinched it for me. I'm going back to Python, and I'll look into Pyjamas to help with my JavaScript challenges.