Wood pro's - it's cheap, easier to cut and generally easier to fasten. It's readily available in all kinds of sizes. Con's - it rots and finishing it to prevent rot is a pain. It's going to rot eventually, just depends on how well it's waterproofed. It's heavier than alum and dimensionally it takes a bigger piece of wood to make an equivalent structure to alum. And because it's bigger it uses more precious room under the decks that could be storage.
Aluminum pro's - it's light and will last forever. You can save room over wood because it is stronger relative to wood. Con's - it costs more and is a little harder to get but certainly not that hard. While you can use most woodworking tools with alum, fastening is a little fussier. Welding is ideal but riveting also works well.
Go with alum if you can. Be creative as to the sources. On guy here used a discarded aluminum ladder for part of his structure. Do a little dumpster diving. Old store fixtures sometimes are aluminum. Visit your county highway garage and see about buying old road signs. One guy here suggested going to your local window and door shop. They will often have seconds of extrusions they can't use to make doors and windows. With the price of alum scrap being high many are now just scrapping their left-overs but if you can intercept it before it goes and talk to the right person, maybe a $20 bill or two will get you all you need.
Lastly, scour the posts here. These guys are really good at making do and being inventive. You'll save a ton of time and heartache looking at what the resident geniuses on Tinboats have to offer.