My Litespeed Tuscany has such short chainstays that my tire nearly rubs the front derailleaur bracket. My Lemond Poprad has longer stays, but not really long like on some touring bikes. The Litespeed climbs much better but I think more than anything it is because it is lighter, with lighter wheels and tires.
I think the chainstay length will have more effect on the ride in general than on the climbing.
Does anyone have a light bike with long chainstays?