Ableton (or any sequencer) vs. Traktor (or any vinyl-style DJing app) is pretty easy to sum up, in my opinion.
If you want to pre-setup all of your tracks, split them into loops, beatmap them, etc, then Ableton gives enormously more creativity. If you want to mix together random sets of stuff you may or may not have had time to set up in the past, then Ableton is, in my (moderately experienced) opinion, basically useless.
I have seen Sasha DJ live several times using Ableton, and I was privileged enough to watch him play a 7-hour set at The Key in London in July in front of about 300 people, where I was conveniently stood 6 feet from The Man Like, and (while thoroughly enjoying myself) had a very good look at his setup and how it works. I've also seen James Zabiela use Ableton in an entirely different way, using it primarily as a very smart sampler and sequencer, to play parts of his own tunes, acappellas etc. Both of these DJs still regularly use CDJs, and in some cases Vinyl (although less and less). Sasha claims that using Ableton is simply an awful lot of hard work, because he works almost entirely with sets of loops chopped out of tracks, as opposed to the entire tracks themselves. He has a team of people working in an office to chop up and beatmap tracks he receives, and his Ableton Live Sets are scarily busy-looking affairs, usually spreading hundreds of loops and samples over 6-8 channels. Sasha uses the CDJs in long sets as a means of having a period of slightly easier track selection to give himself a rest, although for his set at The Key was performed entirely on Ableton as far as I could see.
