To me, a big advantage of screws is that they make it easy to replace damaged wood. For example, if you install a post and you attach it with screws and the post starts to crack, you can replace the post without too much difficulty because the screws can easily be removed. If you used nails, it wouldn't be so easy. Another very important property of screws is that they have more holding power. They really grab the wood because the threads of the screw cut into the wood giving it a nice solid grip.
On the other hand, the advantage of using nails is that it usually takes a lot less time to drive in a nail than it does to screw in a screw, especially if you have a nail gun. For example, if you were going to attach lattice or 2x2s to the top of a pergola, a nail gun can get the job quickly.
So if you have a nail gun and the task at hand requires many nails/screws, use the nail gun. Otherwise, use screws. Stainless steel nails/screws are common for outdoor use.
