This question has been asked in DIY here, but there are several structural related considerations that are worth mentioning for woodworker's consideration.
Most residential codes require nails. That is because the industry standards for nails are well established. The most commonly used framing nail is a 16d and the thickness and material strength of the nail is defined. Any structural wood framing member is going to pass thru load stresses in compression (squeezing), tension (pulling), shear (across the profile), and bending. If you look at common construction screws, the profile thickness is thinner and the metal material type is not the same. My experience is that the screws are more brittle and I have had the heads or bodies snap during installation. In my judgement they will not stand up to the forces that can be generated in a framing situation and I would not use them unless they were certified as structural framing replacements for nails. (I've never noticed such a claim on screws from the big box stores.) In addition nails in a nail gun install much quicker than screws. On the other hand the threaded screw draw pieces together very well and I do use them for non-structural conditions all the time.