There are some pro's and cons to both ...
Nails
Pros
Quicker to lay the boards than screws (assuming you use a nail gun).
Quite long lasting nowadays if you fit galvanised.
New ring annular nails grip well when fitted.
Tend to be better hidden in the board
if fitted correctly.
Cons
Almost impossible to get a board up without trashing it.
Boards will loosen over time as a natural consequence of the expansion/contraction of the boards.
Screws
Pros
If boards loosen over time they can be tightened.
Boards can be lifted and re-fitted without damage.
Screws are generally considered more secure fixtures.
Similarly long lasting if you use proper treated decking screws (Spax say) and far superior to galvanised nails if you use stainless steel.
Cons
More time consuming than nails to lay boards.
More visible than nails but stainless steel screw heads actually look good IMO ... Keep the screw lines straight and you'll get the same neat effect as a ship's deck.
It's easy to shear screws if not careful (particularly if you hit a knot in the joist).
Most pro-fitted decks you'll see in this country nowadays will be nailed wheras most DIY decks will be screwed ... This simply reflects the fact that the pro has the necessary (and expensive) tools such as the Paslode gun to drive these large annular ring nails and fitting time is an important consideration whereas most DIY'ers have power screwdrivers and have all the time in the world
I always personally use stainless steel screws to fit deck boards though I always use power driven annular ring nails to build the frame (toenailing joist to beams for instance where 3" nails are required). One interesting point which often surprises people is that it is no more expensive to fit stainless steel screws bought in bulk (at least 1000 at a time) online than it would be to fit something like SPAX deck screws bought from the sheds. This obviously only helps DIY'ers building medium to large sized decks but is worth considering ... I would never fit the cheap deck screws you see at the likes of B&Q in the big plastic bags ... Something like 50000 screws for £2.50. They shear more often than they don't and corrode like a 1970's Skoda
It is really a matter of you get what you pay for here.
Bottom line though is that Thermo is absolutely right ... It's a matter of personal preference and circumstances and both fixing methods should survive for the useful life of the wood.
Hope this has been helpful.