Can someone explain cassette sizes, and what are the pros/cons of the various sizes?

For example, I have triple, 12-26, 8 speed....while a buddy has a double, 13-26 8 speed. He has problems on the steep hills more so than me, but I don't quite understand why?

Thanks ahead of time!

You have the same low gear in the back - 26t, but you have a lower gear in the front. A triple gives you a 30t small ring in the front, a standard double is 39t, a compact double is 34t. So, no matter what, your friend will have a harder gear for the hills.

The difference comes up front(triple vs. double). His lowest gear is probably something like 34 to 26, where you might have 26 to 26. So, his lowest gear is about 50% higher than yours.

The advantage of a 'taller' cassette, like 11-34, is to have a broader range of gears. The advantage of a tighter cassette is the ability to make small jumps between gears, and dial in the perfect cadence.