I'm seeing more and more beautiful uses of animated GIFs with very smooth playback – the likes of which layer/frame animation in Photoshop could never produce. Just wanted to poll the community to see what are people using for building up animated images (whether GIF or APNG)?

A few recent examples I've received:
Moo's sale reminder
Invision's weekly digest (UX design tips block)

I have access to Flash and After Effects, just not much time to play around yet. Could obviously convert video clips to GIF, but for non-live-action animations or on-boarding graphics, I'd really like make them smoother, more life-like... so just curious, what are y'all using?