ActionScript 3.0 is based on a draft of ECMAScript 4. At first glance it has more of a resemblance to Java than JavaScript (unlike AS2). ActionScript 3.0 is very much a class inherited language and designed around OOP principles. AS2 also has classes but prototypes feature strongly (although I am a little unclear on this area).
AS3 is also a strict typed language. Before you could write code such as:
var a = 12;
and you still can with AS3, the difference is if you were to write:
var a:int = 12;
with AS3 you will get type checking (helping to keep errors at compile time rather than run time). This can also result in a performance increase. Speaking of performance increases, AS3 runs on the AVM2 which significantly increase speed.
There are also a whole host of other features added to AS3. A much improved event system, better XML handling, the ability to load and save to local (FP10), the ability to use Pixel Bender (FP10).
You probably won't notice a huge difference if your doing mainly animations with some code, but still, it makes sense to go with AS3, especially if you find yourself getting more involved with it later on.