Does Everything search file contents? I've only used Everything for searching filenames (and it is fantastic for that). Google Desktop's sweet spot was searching within files.
The stable version cannot. 1.5 Alpha can do it. It can also index properties (as in resolution, author, song/movie length, etc.)
So far I would recommend that one, it has tons of new features (including a change journal that shows renames, moves and deletes in real time) and I didn't experience a single bug yet. And it is even faster.