Summary
Google Wave is designed to replace email, IM, wikis and bogs. It is not designed to be another Facebook, although it will take away some "eyeball marketshare" from the likes of FaceBook.
Analysis
Google Wave is designed to replace email, instant messaging (IM), wikis and blogs. It is build to be a collaboration tool. FaceBook is not build to be a collaboration tool, although if you know your way around it you can use it as such. In other words FaceBook is just a glorified IM platform.
All that Google is trying to do with Wave is to present yet another interesting web application (like Google Maps) that will let users spend more time looking at a Google web page and take in all the ads on the page ("glueing the eyeballs to the we page"). Once the Google technology figures out what you are discussing in your Wave then the ads will be targeted perfectly. You have a Wave discussing your trip to Tahiti and then boom ads for flights to Tahiti and for hotels on Tahiti will appear.
So yes Google is competing with FaceBook by trying to steal their eyeballs but Wave is not just another FaceBook lookalike.
Analyses are solely the work of the authors and have not been edited or endorsed by GLG.