I'll chime in for the pannier side of the soon ensuing debate:
I like panniers because of the organizational aspect; food always goes in the front left, raingear in the front right (both of which I can get at without dismounting the bike), etc. I find the bike handling on bad surfaces or downhills easier to deal with using panniers than a trailer. I also find them much more versatile in the camping sense: can be converted to a backpack with a few straps, can be sat or knelt on on wet ground, can separate wet gear from dry gear easily, can be used as additional insulation from the ground if it's really cold, etc.

Also, I just think they look cooler