What do you like best?
I have been working with After Effects for years now. It's layered design was an easy stepping stone from Photoshop and the potential seems limitless.
This program lends itself well to animation, motion graphics, timelapse, visual effects and accepts plugins from many devleoppers that only add to it's possibilities.
The addition of scopes within AE has really improved my workflow and save me a trip to adobe or using the outdated Color Finesse effect.
What do you dislike?
After effects needs a better workflow for straight to broadcast material so I dont need to go back in to premiere to export a commercial. For example: 24 bit audio isn't possible from within After Effects.... only if I bring it into Media Encoder or Premiere. Neither is MXF export.
It would be nice if Audio mixing was rehauled a bit. I suggest something like a specific audio track where you can mix clips and music instead of treating them like any other object.
Speaking of objects... importing from Illustrator should work better. For example, if you import an Illustrator file... it imports as images. If After Effects has paths already shouldnt it be able to recognize the object paths and keep them to manipulate within AE? Seems backwards.
Playback/rendering should be more intuitive. Perhaps an 'auto-optimize' button that adjusts your settings depending on your computer. I always have this feeling with After Effects that it's not using the computer's full potential, even though I've already adjusted all the relevant settings.
Recommendations to others considering the product
Copy/Paste paths from illustrator into solid layers in After Effects... makes for great vector animations.
You can import Photoshop files for animating. So if you're more comfortable in Photoshop, set up your scene there and animate in AE.
What business problems are you solving with the product? What benefits have you realized?
Beyond just animation for commercials and show openers, we are able to use After Effects to make virtual sets for our producers using plugins like Element 3D. It's astounding what you can do with it.
Colleages have told me that back in the days of analogue effects they would have a million dollars worth of equipment to do effects, and After Effects does all that and more.