http://rockman2ips.tripod.com/index_en.html#mm3
I have not played every single mm 3 hack in existence, but i really liked Rockman 3 Alpha alot from 2007. That was clearly the best mm3 hack out there during it's time before stuff like Minius Infinity ever started
But it does not have new graphics, no music edits, just AI, palletes, level design.
It already was TAS'd by a person though.
ATW is bad, i couldnt stand to play that hack after a couple levels, people felt the same way on the acmlm board dicussion thread when it was first released
Battle of Gamma is pretty good, anything by DurfarC is good.
Almost all by author "chiko" is to be avoided. See "insectduel" 's youtube videos.
The bottom 2 chinese ones directly above burst chaser i have never heard of those 2, so i have no idea whatsoever. nor have they ever been mentioned on the japanese 2ch remodelling rockman thread.
I have not tried Anadanstoon's megaman 3 indonesia hack, it does have new graphics, changed songs (i think), AI edits, and level design. However, his most recent hack, megaman 5 indonesian artifact has gotten great reputation, and i enjoyed it alot too, as it's his best one he's done to date.
But some people dont like the music choices i've seen in youtube comments.