If you're pretty familiar with how a Stratocaster and a Les Paul sound, you can tell the two players apart by their tone. The tone of Clapton's strat is thinner and pluckier. Also, I'm pretty sure that Duane Allman played all the slide, so if you hear slide, it's Duane.
One more thing to consider: if there are multiple guitar players, it's kind of a recording convention to keep them panned to the same side of the stereo image throughout an album. So if, in one song, you've identified Clapton coming out of the right speaker and Duane coming out of the left speaker, then on the other songs it'll probably be the same players on the same sides (I'm not positive this is the way it is on the Layla album, though).
I agree with others that Duane probably played the tastiest licks on that album. I'm pretty sure goosebump-raising outro solo on Layla is all Duane. On the other hand, Clapton's solos on Bell Bottom Blues are really pretty, and he positively burns it up on Have You Ever Loved a Woman. I guess I'd call it a draw.
Yes and yes. I've seen pics of him playing both Teles and assorted Gibsons.
As far as "Layla" is concerned, Clapton played his beloved Strat "Blackie" on the entire album (I believe) while Duane used his '58 or '59 Les Paul Standard. Again, I've seen photos of Duane playing a Strat and Clapton often uses Gibsons (335s, Les Pauls, SGs and even Explorers) both live and in the studio.
It is really impossible to say with definate accuracy who was responsible for each solo on "Layla." Even Clapton can't recall (heroin, cocaine and alcohol were endemic in the studio during the recording sessions).
As a rule of thumb, Duane likely played most of the slide work and likely used his Les Paul whereas Clapton likely played most of the non-slide solos and likely used his Stratocaster. (I say "likely" as Clapton is an accomplished slide-player in his own right and Duane can solo well himself.) Both contributed to the rhythm parts.
I'm currently looking into the history of "Layla" on the net and will gladly let you know what I find.