To be honest, they're both the same. It's like saying, should I buy a Toyota or a Honda? The functions are all the same, but the controls and knobs are probably placed in different areas but they do the same thing. At the end of the day that's what it comes down to, cause either car can take you from Point A to Point B easily.
All I can say is this, pick ONE and learn it IN AND OUT. That's all that matters.
I will say this however, FL Studio is the better software for the beginner, it's layout makes it much easier to pick it up and go. Not to say that Ableton isn't easy to learn, cause it's also very simple at it's core. But FL Studio's interface is much more straight forward with a much easier learning curve in my opinion. Ableton is really good if you want to get REALLY technical with your sounds and parameters, you can do the same with FL, but Ableton makes that much more simpler for the user.
I started using FL Studio when I first began making beats, I loved. Then I bought a MacBook and I decided I'd try out every DAW until i found one that I loved. Ableton was it. I still use FL Studio from time to time, I do a lot of collaborations with a buddy of mine who uses FL, but my main DAW is Ableton.
Hope that helps!