Native Instruments Traktor
is dj mixing software while Ableton Live is more production software.
Traktor works like a twin CD deck on your PC and works like so.
Live is studio orientated and works with blocks to say it i a very simple way. Live syncs BPM automatically so beatmatching is not one of your tasks. You can live remix tracks by adding layers with breakbeats etc to playing tracks.
Live can also be used in another mode so it can be used for productions and remixes.
If you want to DJ : Traktor, if you want to produce : Live.