It depends upon what kind of animations you want to do; character animation, or "grav-car soaring over a vast city containing thousands of huge buildings" kind of animation,lol. I have both applications. Animation Master is a superb software for making and rigging your own original characters, but since the modeling is spline-based, it sits in its own little universe and does not share well with other apps( i.e. polygon-based modelers/renderers) and if you want original props and characters you will likely have to build them from scratch, though A:M does come with props and characters you can learn to animate with. 
    Carrara might have an advantage in certain areas. Nearly anything you build in Carrara can be used  by other polygon-based apps/renderers including the majors such as 3DS Max, Maya, Lightwave, Cinema 4D, and other apps such as Poser, Vue, Bryce, and now Terragen. Carrara can also use nearly any prop(or character) made within all those other apps. 

      Both apps have instances, particles, and physics, and advanced rendering functions. 
I would say that if you wanted to do a character-driven animation with more close-up, or medium shots, A:M might be your best bet. It has better character-rigging tools at this time.
If you want to simulate large machines or landscapes in the real, or Sci-fi fantasy worlds, Carrara might be the better bet. You can use the output of both apps for compositing
with real-world actors, or for match-moving, but here again I would give the nod to CarraraPro.
This is all my own opinion having worked with both apps. I love 'em both. HTH  Dan