Well Ableton is very capable and I'd explore it's mastering plugins before necessarily diving into another DAW... but it was originally designed to be almost complimentary to studio DAWs and was seen as a live solution rather than a studio solution.
However, the lines between live use and studio use have blurred somewhat over the past few years. Ableton Live is used by many as their primary studio application and with good results and many others do what you mention: compose, arrange etc in Live and then export to Logic/PT/Cubase where they mix and master.
Just that out of the box it's effect plugins are not as highly regarded as Logic's... Cubase is a very good DAW to use... I might be biased towards Logic (nothing to do with me being an Apple Logic Certified Trainer ;). I haven't as much experience with Cubase as Logic, but the recent experience I've had with Cubase has all been extremely positive.
Check out these tuts: (yup, there's a Mastering in Cubase tut you may be interested in too!)
http://www.macprovideo.com/tutorials/cubase-application
Hope that helps
Rounik