So after having some experimentation and utilization of the tutorials, I must say, the power of this program is staggering. Frankly, it allows me to transition scenes in ways that are simply not possible in Premiere, and often, it's easier to do too. I see no feasible way, for me at least, to add stuff at the end after arranging scenes in Premiere, like some people say they do. The way I'm approaching it is making mini compositions and then sequencing them in Premiere afterwards, because I tend to work on different segments of a video at a time. The only problem with this method is that when you try to sync something to music, you have to RAM preview it every damn time. So yeah, synching scenes to very specific beats in Premiere is easier, but the actual transitions are done better in AE. Point is, I find myself going back and forth, but I really like the program. I believe I can make better AMVs with this and Premiere than with just Premiere alone.
Anyways, that's my very limited experience with it so far.