Its really a disservice to both artists to compare them, they were both in their own lane, outside of eccentricity and popularity plus the fact that they were both hot at the same time they made different music. You can like them both without shytting on the other, or you can like one or the other based on personal preference, but as far as the comparisons go here's my thoughts:
-Singing: MJ obviously has the more unique voice where Prince relies more on vocal stylings (crooning, falsettos, amplification, baritones). Both typically sing above their natural register but theirs styles are almost completely different. As far as their influence goes, many artists try to replicate MJs inflections but he's got a one of a kind voice. As big as MJ was/is, in actuality, more artists have had success replicating Prince's vocal styles, particularly in the Neo-Soul realm (Bilal, D'Angelo, Musiq Soulchild, etc.)
-Dancing: So there's really no comparison here, MJ pretty much revolutionized contemporary dance from both an artistic standpoint and with his showmanship. Everyone replicates MJs moves, albeit MJ was totally influenced by Fosse, Jackie Wilson, B-Boy Culture and James Brown among others. I will give Prince this though, his moves were a lot more natural and a result of him interpreting the emotion in the song. MJ makes you wanna get in the middle of the dancefloor and put on a show, Prince makes you wanna grab your chick and rhythmically intertwine bodies.
-Songwriting: Contrary to popular belief, MJ is just as much of an influential songwriter as Prince. The big difference is Prince pretty much wrote ALL of his songs where MJ was a brand with a team. Another difference in why perhaps MJ is overlooked as a songwriter is that the reason you like the songs MJ wrote more than likely had less to do with the lyric and more with the inflection where Prince captivated you with the things he would say and the risks he took.
-Musical Acumen: Prince definitely gets the nod as a multi-instrumentalist and what he did for the game from the perspective of syncopation, use of synthesizers and oh my God it's so commonplace now we don't even realize that nobody was doing what he was doing with the snare before him and it's a travesty! I will say this however, and maybe because we weren't really let behind closed doors to watch MJ work in the studio, but he's just as much a 'producer' as Prince. If Dre is producer, MJ is a producer! If Quincy Jones is a producer, MJ is a producer!
I can't find the videos, but I know Quincy Jones has some footage and I've heard outtakes as well, but my life changed when I heard MJ beat box the initial foundation for "Wanna Be Starting Something". Same thing for "Another Part of Me" and the first draft of "Working Day And Night" with him and Janet and other folks using random household objects/percussion ala Jimmy Fallon & The Roots to map that song out. Dude would walk into the studio and physically dance or actually beat box (ala Timbaland)the structure of a song for his musicians to translate into notation 
. I didnt know he had a substance abuse problem. Then he almost fell off the stage.
I hate to laugh........O, dear, I hope hes alright
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x20
in the middle of the floor. a lot of youngins don't know that this is where michael jackson debuted the moonwalk. he had never done it before motown 25. this is the absolute GOAT performance.....
for this but damn if it aint fitting...