Ryan, The software works well with either choice. You can't really go wrong as long as you know how to use either of them.
If it was a simple picture in picture, I wouldn't bother going into After Effects - just because I slow down a little when I go in and out of After Effects. Yes, it's just a few more button pushes, but seconds add up.
What you are talking about is "motion tracking" or using a "corner pin" effect with the picture in picture. Depending on how realistic you want it (and how much time you have), you might want to do other things to make it realistic, such as add a small light glare that moves across the screen or (if it's an old "non-flatscreen" monitor you are putting the picture in) adding a slight bulge to the track to make it match the surface curve of the original physical screen.
For most of that type of stuff, I'd still use Avid FX, but a good AE artist can really make it believable. Six one way, half dozen another - just use whatever you are more comfortable with - or if you have time and you want to use this opportunity to learn and stretch use the one you aren't comfortable with. ;-)
It takes longer in AE but, because Avid never fixed their aliasing problem, ya gotta do whatcha gotta do.
It's funny. Avid released the 3D DVE with MC v5. Whie it was aliased, it was a huge upgrade from v4. Now, more than 15 years later, they are back down to version 4 and boast the exact same aliasing that began biting them in the ass more than a decade ago.
I look forward to seeing where things end up with em. Who do you think will be the benafactors (bisedes us). Apple?
hard to say. The plan obviously is not to compete at this point but to sell.