Rebuilding an exterior deck is it better to use screws or nails?
Not the best answer, but:

Use screws on the top boards where people will be walking barefoot.  Every kid has had a wicked gash from nails (naturally) poking up a bit.

Use big a** nails to attach your cross beams to your main structure.  Nails are only good at holding against a shear, i.e. nails should always be (and only be) parallel with the ground. 

Use large lag screws to hold together your 4x4(?) frame, the main, big parts.

Your deck will experience changes in temperature and the wood and fasteners will not adjust at the same rate.  You want some give in a deck because of this.  You also want some give because of the sporadic forces that humans will put on it.  Nails provide some give.  Screws provide absolutely no give; they will destroy the wood around before they back out.  

Putting screws on the "floor boards" will wear out the boards faster, but in my opinion that is the sacrifice to prevent injuring the fragile humans.

Please also see this question.  Those people are much smarter and concise than me.