Though I own and love logic (it's a beautiful linear composition program) but there hasn't been a serious update in a while as the development team has broken up (I hear). Scary because Apple has a habit of changing radically... but I could make good tracks with it, it's built for linear recording and has some great features like deep rerouting, good busses... hell I may keep it for just final mixes (no new copy).
But Ableton is quite different, it's got the pattern-based "clips" composition feature which makes it much more powerful and fun to create with.
In logic, I would use the "Loop" tool to work on sections, then move/copy the sections and finalize the composition... like an oil painting, getting each part just right. It makes linear composition easy.
Mainstage seems more for gigs... people really like it... perhaps you enjoy actually playing and gigging and might even play keyboards pretty well--I on the other hand have played mostly guitar/bass for years and was serviceable on keys, but sadly had a tiny stroke a couple of years ago and now play keyboard fairly poorly now (I wouldn't pay to see me).
Thus I have been working with electronic music to get my hands out of the equation, looking at what the kids are up to... DJs and EDM, what type of systems and methods are happening. DJ's are changing how music software is made and used and after years of jealousy and vitriol... I'm as bad as they are at playing music (though I feel I know WAY MORE about composition). This is REVENGE as I am using their shiny new tools and having FUN... Muhahahahahahah
Ableton Live has been serving the DJ market for years now, and they have made their pattern based sequencer very, VERY powerful. Ableton Live is a lot like Cubase but WAY more fun.
It is changing the way I compose! I can make sections, passages, change elements and recombine parts ON THE FLY while the sequencer is chugging! Each synth has it's own channel, but one can hold several parts (clips) for the verse, chorus, breakdown that one can access at anytime... you can re-order the clips, recombine parts, extend jams...
... even mix odd time signatures and effects.
All this WITH a linear composition area behind it all to finalize the work if you so desire. So I lose nothing but money on this change over. Only used Logic for a year, so I can move away from it with no real musical loss.
My Korg Prophecy and k2500R (and Cubase) are now gathering dust because my new rig is all on my mac! I have a tiny Akai MPK25 a Nano Kontrol mixer. I only need one plug and headphones!
And its all BETTER THAN EVER!!
. I agree that Apple has left a lot of us scratching our heads. Their direction seems to be away from the more traditional desktop based systems, and toward smaller / mobile platforms. Maybe they'll release Logic for the iPad some day. 
I do in fact use MainStage primarily for gigging / live play. Your description has me wondering of Ableton wouldn't be something to scout out. Heresy