Which would be Fripp, of course. 
This could get ugly very quickly.
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No, it would be Mark Knopfler! 
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There only one way to not settle this!
Well actually there are a lot of ways, but this one involves posting video/music links.
And if @Giltil doesnāt pick Telegraph Road, heās wrong.
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Tough question. A lot depends on what criteria one is using. But if I go by āWho do I wish my playing most resembled?ā, I might choose this guy:
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Iām not sure Fripp was even the best guitarist in that band. 
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John McGeoch, of course.
The piece of Sultan of swing starting at 6 min is a great one
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I lack sufficient expertise to nominate people for this honor: in the company of intelligent humans, this disqualifies me for any role other than reader; in the company of Republicans, it makes me a legend worthy of a cabinet appointment.
I can offer anecdotes though: when I was an evangelical (starting in the 80s), a common tale (retold with faux certainty and received with hushed awe) was that Jimi Hendix was once asked āhow does it feel to be the greatest guitarist in the world?ā and he answered āyouād have to ask Phil Keaggy.ā While this was, like nearly every evangelical cultural trope, false, it does suggest that one or both of those artists could compete for the honor.
The other story (I havenāt checked its veracity) was that the manager of Van Halen insisted that Eddie Van Halen play (at least some of the time) with his back to the audience because they knew that other guitarists were coming to the shows to try to figure out how Van Halen did what he did.
As for my favorite rock guitarists (this is different from āgreatestā of course), Iām of the 70s cult of Fleetwood Mac and the Eagles, and later the (actual) cult of U2. My favorite guitar performance is on the album version of Let It Be; George Harrison correctly worried that the radio version lacked spice, so he added some. Iāve been known to listen to that song 3-5 times in a row in the middle of a tough day.
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It would far too easy to start an argument with myself - and lose! 
Iāve seen Adrian Belew several times, most recently with BEAT, and ā¦ oh look thereās Steve Vai!
Another worthy addition!
The best part: This is not a zero-sum game. 
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This one, from 4min to 5min45, is also quite good.
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Might I suggest that first we should discuss our subjective criteria for choosing ā because lacking some degree of consensus in that criteria, weād end up simply talking past each other.
That strikes me as a tad idiosyncratic to develop a consensus around.
Two criteria that immediately come to mind (though I am explicitly disclaiming that they are the only or the best criteria):
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Pure virtuosity.
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Ability to employ this virtuosity to evoke a strong emotional response from an audience.
Personally, I tend to favor the latter criteria, even acknowledging that this inserts a greater degree of idiosyncrasy, which is perhaps why I tend to favor the likes of Brian May and Eric Clapton, as well as expressing a strong enjoyment of a large number of other guitarists (Mark Knopfler on the Brothers in Arms title track and on Going Home from the Local Hero soundtrack immediately come to mind).
I was surprised, on first watching this performance, as to how accomplished Prince was as a guitarist:
However, although I am perfectly happy to acknowledge him as a great guitarist, his work doesnāt resonate with me sufficiently to feel any inclination to advocate for him as āthe greatestā.
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Eric Clapton
David Gilmour
Jimi Hendrix
Carlos Santana
Jorma Kaukonen
Duane Allman
Steven Stills
And sure, Mark Knopfler. First time Iāve agreed with @Giltil to my knowledge.
But I could defend any or all of them, depending on the moment. Objective, most definitely.
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It makes me sad how often Gary Moore is left off lists like these. He must be the most underrated guitarist of all. Just watch the virtuosity and feel the emotion in this:
For me he was the best.
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Iām surprised this guy hasnāt been mentioned yet:
Strictly in terms of virtuosity, I think Allan Holdsworth was one of the most virtuosic musicians to ever play the electric guitar, though he might be considered more a jazzer than a rocker. That legato!
That said, I wouldnāt consider āvirtuosityā (in the sense of the ability to play scalar passages at fast tempo) a sine qua non of a great rock guitarist. @John_Harshman has mentioned John McGeoch as an example. Keith Richards is another. Intangible qualities like āfeelā and āattitudeā can be at least a important as technique. Sloppy often sounds better than impeccably clean;
I consider Neil Young a great rock guitarist, though he is far from a virtuoso:
Sometimes, though, sloppiness and virtuosity can happily co-exist:
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I didnāt, but Iād say that Stephen Stills, whom I did mention, fits that criterion.
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And the problem is???
But those arenāt a bad place to start the argument. More on that later ā¦
I was surprised, on first watching this performance, as to how accomplished Prince was as a guitarist:
Oh yes, Prince was a kind of musical genius. Even people who donāt care much for his music acknowledge that.
I was about to mention JB, but got stuck in in traffic. 
Hendrix was a late arrival too.
Speaking of Traffic ā¦ Winwood? For me he is more of a composer and vocalist, but some rank him among the best guitarists.
Sister Rosetta Tharpe should not go unmentioned.
Nor should Joan Jett and Bonnie Raitt.
Iām a big fan of Joan Jett, but would not suggest that she charts in this respect ā she āworksā more on attitude and energy than on any technical prowess (both instrumentally and vocally) ā closer to the āpunkā aesthetic. And although Crimson and Clover is probably my favorite track of hers, I donāt think the above clip did it justice ā a rather lackluster performance. Sheās much better in the following clip:
