Best blues guitarist, Clapton or Green

I wouldn't call Hendrix a blues guitarist by any means. He could certainly play a blues and add his specialness to what he played; witness Red House and Voodoo Chile but he did not front a blues repertoire and that was the focus of this question.
In my humble opinion, many of the responders to this question are including fringe blues players that are really more rock n roll. Blues is more than a few songs it's also a lifestyle for the men and women who can really be called blues players. To me, the artists that have had longevity and consistency with the style rather than exploring other genre better fit the question being asked.
I saw BB king in the 60s and again last year, he epitomizes the consistency I'm referring to.

REL2

How about Quicksilver Messenger Service's version of Happy Trails???

Stevie Ray Vaughn vs Eric Clapton - I have read through this thread and am amazed at the SRV fans. I can't help but to remember when I heard both SRV and Clapton (live) within a month of each other at the same venue in the late 80s. I'm sorry SRV fans but in comparison SRV sucked! It was so bad that I considered leaving. I don't know if this was around the time Stevie was bottoming out on booze, but he was really bad. Clapton, on the other hand, was great(I've seen him 4 times in concert). Incidentally, I saw SRV first. I was looking forward to SRV as I liked his albums, and his reputation as a great guitarist was building by then. Albums aside, nothing shows what a musician is really made of but a live concert.

John Cippolina, now there was an interesting musician. How about "The Fool"?

Muddy Waters
Buddy Guy

YES, Jimi Hendrix was a blues guitarist. From whom did he learn? In whose band did he play? Buddy Guy!

Eric Clapton and some other names are great "blues-style" guitarists, but are not "blues guitarists."