I gotta echo what Ski says here and emphasise that you can make excellent music using any DAW out there... Logic, Ableton, Cubase, Pro Tools, etc.
I'm a self-confessed Logic Nut and find it great for composition, sound design, mixing and love tinkering in it's environment...
Live, apparently, doesn't have as good a sound engine as Logic... but the same has been said about Pro Tools... but it's arguably the industry standard.
I'd recommend checking out the videos here for the Live 8 101 and the Logic 9 101... (even with a free account you can watch the first 10% of any tutorial) to get an idea of which you warm to quicker.
(Click on the Watch Tutorials button at the top right of this page).
I'd say Logic does traditionally have a steeper learning curve than Ableton Live - but it's become much easier for new users for the last couple of versions. I personally found Live more tricky to get my head round than Logic... but then I've been using Logic for over 8 years.
Instrument and Effect Plugins wise - both are excellent - and both are used by House Music makers the world over. Live might be a bit more "instant" for beat making...
If you're looking to create dance based music in the studio and play your music live then Ableton Live is probably the way to go.
Logic Studio is a great price for all the tools you get... but sometime in the future regardless of which one you choose you'll probably want to purchase 3rd party synths and effects...
... you know the more I write, the more I realise there really isn't a definitive answer and I'd say (like with most things in life), go with your gut feeling.
Hope this helps somewhat!