They have Pinkie Pie. Even though she doesn't have the word "party" in her name, she still completes both the party and alliteration trifectas just fine.
There's DJ Pon-3 (aka Vinyl Scratch). This character has no official name, has never said a word and appears for less than 5 seconds out of the entire series 10 hour, 26 episode series; just long enough to magic a turn table arm onto a vinyl record and bob her head a few times. If you do a Google search for "DJ Pon-3" you'll get 155,000 results.
MLP doesn't compare to AT. It's aimed at young kids (5-10) with a few references for their parents or guardians as they watch along. It's honestly a good show for small children, especially considering its a toy commercial, but don't expect anything more than that. It's not even Spongebob, let alone Powerpuff Girls, let alone Adventure Time. Its sophistication is bizarrely overstated by its weirdy fans. Watch the first couple of episodes and unless you are insane you will just walking away scratching your head.
Got the same impression from Avatar. Very well done for a kid's show - maybe even the best ever made - but it's still very very much for young kids and adult fandom is just baffling.