I have yet to even beat PMD2, but my favorite moments in both are
PMD1
When you first join your team
Getting kicked out of town and leaving
The fugitives-on-the-run part
When Absol joins your team (I nickname her Abby ^^)
When you leave (I cry. I don't bawl, but I cry)
That part where you're wishing to go back after the credits.
When you do come back (It was great that there was no dialogue, that was perfect. It would have made the moment cheap if they had talked, I think.)
PMD2
Wigglytuff and his apples xD
Your partner in general, but especially when he's all, "I can't do this." But then something or someone makes him all, "C'mon, let's take this guy down!"
Getting selected for the expedition
Battling Groudon and meeting Uxie, finding the 'treasure'
And a whole bunch of others. I need to finish the game...