I guess the real answer would be the Gift. It's the one that I watch the most, but it's also a sad/happy ending. I find myself finding it sad, but in a happy way if that makes sense. It's like as much as seeing Buffy die hurts, it seems like everyone in the end are happy. Buffy is finale at peace, and so are her friends and family. It's the perfect ending, the only ending, that shows a bright future for everyone. And unfortunately (because Buffy is dead), I think it was also the best ending for Buffy. Not that being dead is a great thing, but when you are the slayer and everything, and after her incredibly inspiring self-sacrificing, I think her going to heaven is the only way she can ever truly be happy while being at peace with her duties. So what I'm trying to say is that the gift does make me the most emotional, but those emotions are not only sadness, it's a mix of satisfaction, happiness, closure, and everything else a finale should be.
As fair as being restricted to which episode makes me the saddest, it would probably be the ending of s6 (although I can count almost the last 3 episodes in that). Willow's storyline is one of my favourite in the entire verse.
For Angel, it's been a while so I have a hard time to choose, but I'd say Not Fade Away but for similar reasons as the Gift.