How long would it take to be comfortable using both? I know it depends upon the person, but would 6 months, with 5-6 hours a week put in be enough?
Oh, I really can't say... "comfortable using the basics of both" maybe? They are both quite deep if you want to.
Logic is probably the easiest if you have seen a midisequencer before, it works like sequencers have done for ages.
Ableton Live have a bit of a different GUI with the "session view" as the main composing area (it looks more like Logic in it's other view - "arrange view").
It all depends on what you want to do. You will
probably be able to learn the basics and get around quite comfortably in both apps in half a year.
(really understanding and programming all synths yourself, know how to use eq, fx and mix well is more of a lifetime project...

)
For me, coming from "traditional" midisequencers and mostly making various forms of electronic music, I still prefer working with Ableton Live nowadays even though this program is the newest one for me. It's so quick for trying out new ideas and quickly get somekind of a rough sketch to keep working on. Ableton Live's dead easy mapping for midicontrollers can't be matched on any other digital audio workstation as far as I know. Ableton Live could be used as an whole instrument for live performance jams and recording of them.
I use Logic for working with older projects where hardware synths are involved. I prefer Logic's mixing and eq-tools when doing audio recordings of my old hardware. Compared to Ableton Live, Logic is more of a studio with instruments and a mixer & fx in it. Suits a more "linear" way of working, when you from the start pretty much know where you want to go.