The answer is sort of both. I may edit an entire sequence in Avid then take it into AE to apply a film look to everything.
Or I might edit a sequence in Avid and decide that one shot needs to be stabalized, so I'll just export that one shot into AE and fix it. No point in rendering a ton of extra stuff, if I'm just fixing one shot.
Also, just to be clear, AE isn't an editing app. It can be done, but it's not made for editing and it can be pretty frustrating to use it as one.
Johnny Cuevas, Editor
"I have not failed 700 times. I have succeeded in proving that those 700 ways will not work. When I have eliminated the ways that will not work, I will find the way that will work."
---THOMAS EDISON on inventing the light bulb.