I can't speak to Aptana but Google App Engine is a radically different development experience from what you'll get with something like Slicehost. It scales differently (i.e. you've got the possibility of handling much larger loads) but it's also totally different than running your own web app server (e.g. Glassfish, Tomcat, JBoss, etc.) and coding using "standard" Java tools.
With Slicehost or any hosted solution it's easy to setup your own development environment locally which exactly mimics what you'll be running on the server. Same software, same VM, maybe even the same version of Linux. You could even move to a different host and still be able to setup that same environment.
With Google App Engine you'll find yourself building on an emulator (you don't really run BigTable locally) so there's not a one to one correspondence between your environment and that on the server. There's no alternative place to move to and still be running in the same environment either. Also, some perhaps many of the popular Java frameworks you might use for a web app development will either not work at all (e.g. ) or will not work out-of-the-box (see here for more details).
I'm not down on the App Engine, in fact, I think it's really cool. If the demand for your apps is relatively low and therefore you're not in need of the huge scaling requirements, but your traffic is not so low that you fit comfortably within the free allowance at Google then I would probably lean towards a hosted solution like Slicehost instead.
