Effective climbing is a function of both your aerobic capacity and leg strength. If you spin up a hill in an easier gear and at a faster cadence, you're taxing your lungs more than your legs. Conversely, if you go the same hill in a bigger gear and at a slower cadence, you're taxing your leg muscles more. I did some hill repeats the other day. It was easier for me to go up the hill in my largest gear than to spin up it in a smaller gear.