mersault wrote:to the OP:
And yes, render each individual track out of LIVE. Export audio, select "all tracks" - that will give you separate audio files for each track. Bring those tracks into your mixing software. ----Even if you're not doing any processing in the mix, this should still greatly improve what Ableton is giving you in the rendered track.
nothing wrong with mixing in another DAW, but I don't want to read this kind of superstitiousness rumours again. Please prove it or stop spreading this misinformation. I tested this many times via phase cancellation and it's just not true.
There are problems in ableton and maybe problems with rendering as Khazul mentioned, but only under special conditions.