For Buffy:
1) Passion
2) Innocence
3) Chosen
4) Becoming, Part 2
5) The Gift
6) Angel
7) I only have eyes for you
8) Band Candy
9) Surprise
For Angel:
1) Not Fade Away
2) I will remember you (could easily have been number one)
3) Hero
4) You're Welcome
5) Destiny
6) City Of...
7) A Hole in the World
8) Smile Time
9) Reunion
Man, this was tougher than I thought it was going to be, especially on Angel. There were a number of episodes that I really, really enjoyed, but I wasn't sure if they were the "best". I mean, it was hard leaving "Halloween" out on Buffy, and "Spin the Bottle" on Angel. Also, there were a few I wanted to pick on Buffy but ran out of space. "Amends", "Welcome to the Hellmouth", and "Dirty Girls" were all favorites as well.
I found on Buffy that I with the exception of "Chosen" and "The Gift", every single episode I picked came from the high school seasons. The episode quality in S2-3 is just incredible. With Angel, a large portion came from S5, which I found interesting because I generally think of S2 as my favorite season, and I only chose one episode from there.
My top four on Angel was just a crap shoot, really. Any of them could have been number one. I also found it interesting looking over my choices that on Buffy, three of my favorites were season finales, but on Angel, only one was. And I had a really tough time leaving "Graduation Day, Part 1" out.