As an uneducated farmer myself, it's easier to 'get' (appreciate) Davies' photos than Corbijn's.
I love his bold use of color in some of them. Others are pensive: moody and beautiful at the same time. It is beyond beauty when he catches the band in an intimate (platonic way) moment, like during the NLOTH recording. You really feel like the fly on the wall you've always wanted to be when it's 'just' the four of them.
He has a way of making the pics majestic. He doesn't just capture the moment, he glorifies it. Some of the moments are quiet (maybe even boring, what the band members are doing) but he really draws you in with them.
I'm sure he's gained the trust of the band too, from all the beautifully emotive Larry pics and this heart-melting beauty:
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Ok, now that I've said some arty stuff, the guy also has great eye for muscle definition and how their muscles catch the light best.
Exhibit A, Adam's biceps:
and of course many other pics. In the this Bono pic, he literally looks beefy with, ya know, a muscular torso!
Last thing, (which I've wanted to say most) he really knows how to capture the boys looking...good. Meaning: handsome in the conventionally accepted way that each of them is recognized as looking. Wow. For instance, he really does Adam's jawline justice, and I'm sure he's aware of that when he photographs him. I don't look at the rest of the guys so much, but... it's incredible that all 4 of them look their best in a single shot. (most of his shots). WOW.