This thread makes my avatar a happy dead man.
But seriously, I couldn't say. As much of a Zappa fanatic I am, and as much as I want to support my vision of him being one of the greatest "artists" of all time (or dare I say, some sort of modern Uomo Universalis?), I don't know what the 'Greatest Musician" means.
The best at his instrument ever? Then you've gotta compare guys like Mike Mangini, Virgil Donati and Marco Minnemann, with guys like Steve Vai, Guthrie Govan and Allan Holdsworth. Leaving out everybody that's operating in different genres (I've seen a lot of people make notice of classical composers, some of which were even just mainly composers, not that great in their instrument)
Is it composing? Then next to personal taste, I disgust Mozart and Bach for instance, but I love Steve Reich or Arvo Part, or even Johannes Ockeghem on occasion, it's indeed a matter of 'who do we know, and why is that guy the best known for his day and age? Most of it has to do with the 'divine support' he got. Apart from that, songwriters, or composers in this modern day (Neal Morse, Roger Waters, and yes there he is: Frank Zappa, Mickael Akerfeldt, Steven Wilson etc.) are mostly assisted by a producer, or a band at least to make what they made.
Productivity is mentioned (Merzbow, Zappa again, may I mention Klaus Schulze?) or progressiveness (Brian Eno, Dizzy Gillespie, Charlie Parker, but also the guys from Sunn O))), maybe Mike Patton even) or 'feel and passion' (David Gilmour, Jonsi, Daniel Gildenlow perhaps, Damien Rice), but all of those in itself are not enough to make a complete musician.
So:
in the tl;dr section:
Zappa.
Playing good: Inca Roads
Composing good: Echidna's Arf (Of You)
Producing/bandleading good: Billy The Mountain
Producutivity good: well, it's a wide range of styles, check out: The Chrome Plated Megaphone of Destiny
Progressiveness: Bebop Tango
Feel and passion: Black Napkins, or: Jesus Thinks You're a Jerk (the second half)