After Effects does EVERYTHING.
I have been using After Effects for the last 7 years, and I keep learning something new.
People often get overwhelmed when starting with After Effects, but that is quickly made up for in its versatility. If you're only working on a small project with light effects, it's well easy to get it done. Likewise, if you have an effects-heavy sequence with 3D modeling/animation, rotoscoping, particle effects, etc, you have an arsenal at your hands.
This is only compounded by how easy Adobe makes it to modify After Effects. Lacking a certain effect? Drag and drop a 3rd party plugin. Don't know how to accomplish a specific effect? Load up a preset. Add in built-in Maya and Mocha, and there is nothing this program cannot do.
The only down-side of this program is how complicated it seems from afar, but this is usually not an issue for anyone getting started in compositing.
Because of After Effects' versatility, light projects have very fast turnover. This is especially important when you are working on a Premiere Pro project that's linked to an After Effects project. Light projects render very quickly, meaning you can get back to cranking out client projects in a breeze.