It's funny. Working at a music store, and as a guitarist, these discussions come up ALL the time. I told a customer once how much I love Clapton, and I got a 30-minute dissertation about how great Hendrix was and what a coward Clapton was (apparently, this guy thought that when Clapton joined Delaney & Bonnie he had joined Bonnie Raitt in order to "cower" in fear over what Jimmy was doing. I didn't have the heart to tell him he had his Bonnies confused).
Anyway, I try to cut these conversations short unless they are ridiculous. When Rolling Stone put out it's 100 greatest guitarists list, Kurt Cobain and Jack White were in the top 20 while Eddie Van Halen was number 70 (which put him behind not only White and Cobain, but also the likes of Ike Turner, John Fogerty, and Jerry Garcia). This made me realize that if those guys can come in ahead of EVH on a list of the greatest, then it is EXTREMELY subjective.
I notice that when I like a guitarist and I am listening to them a lot, I start to notice parts of their playing showing up in mine. When I was recording an album with my band back in the day, I was listening to a lot of Clapton, Slash, Morello and EVH, and you can hear that sprinkled throughout the recording.
Slash and Dean are both descendants of the bluesy rock God, which finds itself intertwining Beck, Clapton, Page, Hendrix, and EVH (yes, he's essentially a blues player), amongst others. But you can see how differently these rock guys can incorporate blues styles into rock. Further, Dean's influences come from a wider variety, going into country, jazz, and bossa nova, as well as classic rock, which is Slash's biggest influence.
I would say that, hands down, I prefer Dean's approach to tone, and variety in tone, than Slash's same old one sound for clean, one sound for dirty.
I prefer Dean's (and moreso) Rob's approach to songwriting and chording than I do Slash's. That's not to say that complex fingerings and arrangements are "better", but to me it shows a better command of the instrument than Slash. The use of jazz and bossa nova voicings make guitar soloing more complex as well. Still, the art of writing a great pop song from the same 3-5 chords that most people use--and making it sound new and/or interesting is a talent as well. In that way, I love songs like Fall to Pieces for their simplicity. Still, a song like Sour Girl is pop-tastic while using more flavorful chords.
This idea, of course, segues nicely into soloing. Some people like blistering, in-your-face soloing. To me Slash is great at this (though he is not as fast as many think--he starts playing behind the beat in famous solos like Paradise City). His approach is unique. His fast runs into solos are great (like You Got No Right or Dirty Little Thing), but sometimes, he comes out of the gate swinging and it does not work (like She Builds Quick Machines). As far as versatility, Slash is more limited. However, he has created famous "licks" in his solos that, if you're covering one, you HAVE to play. There are licks in Sweet Child O'Mine that you HAVE to play. You HAVE to play the end solo lick in November Rain. Slash, being more of a traditional blues player than Dean, is also a more interesting player when "jamming" than Dean is. So, Slash has his strengths and his weaknesses.
Dean, is just much more versatile. He has also come a LONG way as a soloist. He has gone from an average-to-below average solist for most of the first two records into a fantastic soloist on Tiny Music and beyond. Slash would not be nearly as good on a song like And So I Know. Dean's tasty playing has become his hallmark. He also knows when a song does NOT need a solo. A song like Atlanta could have had a guitar solo at the end, but he restrained himself for the purposes of the song. This tells me that Dean is more focused on what the song needs, not how he can fit his guitar needs into the song. Dave Kushner, for anyone that's seen VR live, can freaking play guitar--yet there are solos in almost all, if not all VR songs, and Kushner doesn't play any of them. This tells me Slash has an ego about putting guitar solos into each song. For as great as Dean is, though, if you're not a flashy player today, it is tough to get attention. Further, GnR was SO huge that Slash's signature licks are enjoyed by fans of all kinds of music. STP's fanbase is more limited. Therefore, Dean's signature solo licks are not as vital. To me, the descending lick near the end of Lady Picture Show (the lick that starts E-->D#-->E-->C#-->E-->B in the 12th position) is as vital as the lick in November Rain when covering the song. But everyone in the bar knows November Rain and the end solo, so if you don't play it, they'll notice. Perhaps only a few people would notice if you didn't play the lick at the end of the Lady Picture Show solo.
Because of the hit songs with signature licks, his ability to play flashy, and the fact that his personality is bigger than any band he could ever be in again, Slash will always be considered "better". He'll get the call to play on some dude's record from another genre, or the call to play alongside Michael Jackson, or whatever. It also helps that as a player that wears his blues influence on his sleeve, he fits into almost any situations seamlessly, even if the end result is predictable.
Ironically, Dean seems to repeat himself in jam situations. I hear the same licks on bootlegs when the band "jams". He is not as comfortable outside of the song. So while Slash will get the "come jam" call, his predictable playing in that situation will surpass what Dean would do.
In my opinion, this makes neither guitar player better or worse, just different. But, if I were to pick the guitarist I would rather be, it would be Dean.