Premiere Pro is Adobe's video editing software, whereas After Effects is the compositing and post production package. True that After Effects has editing capability and Premiere has some compositing/effects capability, but when you use the two together, you have a complete suite. On their own, they do one thing exceptionally well and a bit of the other.
I'm far from an advanced user, but after a couple years of casual experience with both, here's how I see them (ratings are contextual):
After Effects| Compositing, transitions & fx - 10/10 | | Editing - 4/10 | Premiere Pro| Editing - 10/10 | | Compositing, transitions & fx - 3/10 |
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