From what I understand (and having tried a demo of it), Ableton Live is a loop-based production tool, similar to Acid Pro, and has a lot of features that make beat-matching and sampling simple.
Everyone who talks to me about Logic always says that it has a very steep learning curve, but is ridiculously-full featured. I'd say in terms of simplicity, Ableton is moreso, but Logic will allow you room for growth as you develop your skills and knowledge of production. Plus, Logic Pro is a good second step after GarageBand, given that they're both compatible as Apple-developed programs.
Please correct me if I'm wrong about any of the above, since I don't use either - this is just what I've heard from people who actually use these programs.
Edit: As a new producer, since we're talking software, I say start with something free, i.e. Garageband if you're already using a Mac, or Reaper if you're on Windows. Save your money until you know what it is that you're looking for and what you want it to do - a lot of us started out on demo versions and things like that before we built out our setups.