They're not competing with each-other... Ableton's a pro tool. Garageband for iOS is a fun app aimed at beginners, which allows one to experiment, record, have fun and maybe even produce some tracks. It's surprisingly capable, although it's focused on loops and presets.

You can think of GarageBand as a simplified version of Logic which is used by a lot of professional producers, so GarageBand is maybe not as amateur as it might seem. More of a simplified entry point into music production to get people eventually into Logic when they get more advanced. Ableton includes a lot of more professional features, but if you want a more serious comparison I might compare Ableton to Logic where you can basically accomplish the same things in each one with different workflows etc.

There are quite some videos out there from famous producers showing their craft, and many use Ableton (Deadmau5, Timbaland) or Logic Pro (Armin van Buuren). It helps develop the buzz.

Ableton is really two softwares in one, for composing and for performing