I don't have an answer to what makes one person a better climber than another. I'm pretty good on long climbs, I am 5'10" and 146 pounds. Not exactly a flyweight but not too heavy either. First I like climbing. It's something that I really enjoy doing, I think that helps. Second once I find my rhythm (tempo if you like) I'm able to hold it and stay with it. What I see a lot of guys doing is going to hard and then blowing up. On a long climb there most likely won't be a place to recover. So many times I've had guys ride away from me at the bottom only to catch and drop them as they faded half way up the climb. Also keeping a nice high cadence works well for me, and staying seated, I only stand to get on top of gear then it's right back down into the saddle.
The types of climbs that hurt me are the short steep power climbs, I've had guy who out weigh me by 40 pounds drop me on the short stuff.