PiTiVi

PiTiVi is the video editor bundled with Ubuntu, and perhaps the first credible “iMovie equivalent” for Linux. I have not used it, but I am recommending it based on the fact it’s bundled with Ubuntu and the quality of its website (which is literally light years ahead of any of its rivals). Judging from its screenshots it looks like at minimum you can do straightforward A/B edits. And, because it’s FOSS there’s no reason to expect it to be intentionally crippled the way iMovie in particular is (e.g. it’s impossible to do any real compositing in iMovie, for that you need Final Cut Express/Pro).

Unfortunately, PiTiVi is not available for Windows or Mac OS X.