What are the pros and cons of each?
The main thing is weight - carbon fibre is lighter.
Another thing to consider if you plan on being really rough with a boom pole is that aluminium will dent fairly easily, so get one with as thick walls to the pipes as possible. Carbon Fibre won't dent, but will crack, you can still use a poll with a dent, once the fibre cracks you either have to replace the cracked section or get a whole new one if you can't find a replacement section.
The difference in weight won't seem drastic on the show floor in a store but will seem gigantic around the 12 minute mark of holding it over your head. Your best bet is to get the most expensive carbon fibre boom you can afford and then treat it with respect, so dents and cracks are not an issue at all.
The obvious difference is weight.