Currently, the Google ads give Clapton three ads and Jimi one, so we know what Google thinks, and that should be the end of it.
But, it isn’t…
You asked for it, so here it goes:
The greatest guitar player in the world must be arguably the best in each of the following categories:
Technical skill - The guitarist most be arguably the best in the world technically. He must have a master’s grasp of basic and advanced music theory and he must be able to play and solo correctly over any key on the fly (not just by feel). He must have a strong grasp of the concept of the scales that compliment the song he is playing in, and he must know his instrument and every note on the fret board perfectly. Ultimately, he/she should have been educated formally in music instead of acquiring his/her skills in a bedroom. Fantastic examples of this are Steve Vai, Joe Satriani, Paul Gilbert, and to a lesser degree, Yngwie Malmsteen. Players like Stevie Ray Vaughan, and Jimi Hendrix (yes, that’s right) do not score well in this category. Clapton gets into this club just barely.
Soul of the music - The guitarist must be arguably the best in the world in using his guitar to communicate emotion and making his audience feel what he feels when playing. He must be a world class bluesman. He must have total tonal control and have the ability to connect his voice to the voice of his audience through his instrument. Perfect examples of this would be Stevie Ray Vaughan, Jimi Hendrix, Eric Clapton, and a ton of other musicians I have failed to name. Steve Vai would score much weaker in this category and Yngwie wouldn’t get through the front door.
Musical innovation / style - The guitarist must be arguably the best in the world in using his guitar to change the way the world thinks about music of any genre. He must be an innovator, someone who is mimicked and who’s trademark style is still being built upon and influencing generations of guitarists. Perfect examples of this would be Jimi Hendrix, Eddie Van Halen, Chet Atkins, and other players that gave a shot in the arm to guitar-based music when it was most needed.
Songwriting - The guitarist must be arguably the best in the world in using his guitar to create melodies that transcend time. These melodies will be a part of the very foundation that shapes the future of music. This guitarist’s work would effectively galvanize itself into the lexicon of music and completely change the path through the thicket. Perfect examples of this would be Jimi Hendrix, Eddie Van Halen, Eric Clapton, and a ton of other musicians I have failed to name.
Perfect timing of death - The guitarist must die at his absolute peak, preferably in a plane crash or failing that, a drug overdose. This is the final element to the perfect musical career, as if you leave the world when you are at your best, you become greater than humanly possible in the conscience of the human collective. Look at players like Randy Rhoads and Jimi Hendrix, both of which owe at least some of their status to their premature exits in life. Think of where Eddie Van Halen would be in the ranking if he had died in a fireball during the 1984 tour. Think of how much better Stevie Ray Vaughan would have been considered to be if he’d died just a few years sooner. A perfectly timed death is essential to being the best.
Your two candidates come from the same stomping grounds. They both have mastered the styles in which they play, but aside from a few notable exceptions with Jimi and experimental music, and Eric and his ability to continue to adapt and be effective in pop culture, neither of them have mastered every musical facet of the guitar. As hard as it is to believe, even Jimi Hendrix didn’t have an ultra strong grasp of musical theory like the Satriani’s of the world. Both of them have had powerful influences on all music that followed them, but Jimi Hendrix managed to pull away from Clapton in this category. Clapton’s work altered the course of music, but Hendrix’s music destroyed what we knew and created a new path for others to follow (as did Eddie Van Halen).
Then Jimi died, and his martyrdom, like a rocket fired into the void, continues to penetrate the deepest parts of our imaginations to this day with questions of possibilities regarding what could have been. Eric Clapton and Eddie Van Halen cannot compete with a ghost that left, presumably just when he was getting warmed up.
Your answer, as far as I’m concerned, is that overall, Hendrix was about 10% better than Clapton before he died. His death accelerated his guitar player status forward exponentially. His untimely death contributes to his status as the greatest guitar player of all time nearly as much as his actual abilities.