Firstly, they were both mad as a box of frogs. And both the product of a golden era in American popular music; born smack in the middle of the century that gave us Jazz, Blues, Gospel, Rock and Roll, R&B, Funk, Soul; to name but a few of the advances in what people could create with a voice and a guitar or keyboard. Both Prince and Jackson were like a condensed and streamlined version of what came just before them. A rich musical diet packed with treats provided by the likes of Little Richard, James Brown, Stevie Wonder, Ray Charles, and later both influenced by the psychedelia of the Beatles and Hendrix.
Seems futile to debate which is better but that never stops anyone around these here forums..
Songwriting - Prince>>Jackson
MJ arguably had bigger hits but was nowhere near as prolific a tunesmith as Prince, which some may argue waters down the Prince back catalogue however Prince had some huge hits amidst the thousands of songs that he released. And furthermore wrote various global hits for other artists. MJ also used songwriting teams to pen some of his biggest numbers. Prince was always at the helm of that particular fundamental.
Musician - Prince>>Jackson
This one's fairly obvious. Aside from Prince's ability to play Piano/Drums/Bass and a variety of other such instruments, his mastery of electric guitar is really second to none. He was a highly respected guitarist, especially amongst other guitarists.
Singer - Prince>>Jackson
When Jackson first appeared in the early 70's, a small child with a huge voice, it was hugely impressive and clearly he had an immense talent. However after his peak period with the "Thriller" and "Bad" albums, he seemed to become a parody of himself vocally. The singing sounded weak and seemed to rely on studio production and an array of vocal quirks that became synonymous with the MJ sound. HEE HEE Shamon! etc... Prince not only has a much more powerful voice, capable of singing belting rock and gospel as well as the falsetto that became a trademark but technically he also has a superior range.
Dance - Jackson>>Prince
Prince was an amazing and acrobatic dancer but he didn't really break any new ground. He was essentially doing a "James Brown" albeit in 6 inch heels. Jackson seemed to have musical control of every fibre in his body. His movement was detailed down to the tiniest twitch and he could "glide" across the floor. MJ was much more switched on to the street dance craze of the early 80's.
It's subjective of course..
but for me personally... Prince Goat