Nails are used in almost all framing and structural applications. Most code books are designed with nails in mind and will have specific minimum nailing requirements and patterns for different applications.
Structural screws are coming more and more on the market every day, but because most code books don't include them you will need an engineer's approval of their use to pass inspection in many cases. If you want to use structural screws without paying the big $$ for an engineer you should talk with your municipal build dept. first to see if they will allow it.
Your normal wood screws are not structural. Standard screws are brittle. If you take a normal screw and drive it part way in and whack it with a hammer, it will snap. If you do this with a nail, the nail will bend. Which would you rather have holding your deck up? Something that bends but stays intact or something that can snap?
I mostly use screws only for temporarily holding things in place while I nail stuff up and for the decking surface.
However, on one deck I built last year I used a ton of structural screws.
I have a couple of times had the head snap off of a structural screw when driving them in, and three of them snap when a small machine hit some lumber. While undoubtedly considerably stronger than normal screws, this leads me to still question their shear resistance.
In the end: nails, hex bolts and lag bolts are still better in most applications. Structural screws are just easier than bolting and cooler than nailing. I do love using them, but they don't (and shouldn't) completely replace traditional fasteners.