The first movie was emotional because A) everything (lives, society, etc) was at stake, and all of that was played seriously.
The first movie was also emotional because Spongebob and Patrick went through a lot of character development- and almost died.
The second movie isn't as emotionally heavy because we KNOW that everything is going to be okay, almost all of the post-apocalypticness is played for laughs, and the character's lives aren't really at stake.
Then again.... what sounds silly on paper could actually be very poignant on screen, depending on how it's drawn and acted.
The emotion that I got (as in the "awww" moments) were nothing comparable to how poignant the first movie was. But there were a couple of genuinely sweet, little moments, and I won't spoil too much.
In one scene, Plankton and Spongebob, who have fled Bikini Bottom, are on the run and on a mission. Obviously they're both stressed-out, and Plankton helps Spongebob get to sleep by putting a blanket over him. (Awww!)
And Spongebob (I won't say exactly) does something genuinely nice for Squidward at the end. I won't say what he does, but it's an "aww" worthy moment.