It depends on what 'the old days' means. Screws are more expensive than nails and easier to emplace. That has been the advantage of nails for most people for a long time.
speed and cost
faster
depends on the wood, nails, screws. but both are ok use
One screws one nails use joints not screws and nails.
Nails are much better to use when putting up a wodden fence.
Fine woodworking is the use of no nails or screws.
can nails and screws be a solution?
You can use drywall nails or drywall screws. I prefer the screws.
use a magnet
Any material containing iron or steel is subject to rusting when exposed to air or moisture. If you pull apart an old fence, you will always find rusted nails in the wood where moisture has rotted them. The modern way is to use galvanised nails or specially coated screws instead. In any hardware store you will see green and brown screws made for outdoor use.
Then you use another glue that doesn't need a glue gun.
They usualy use carpet tacks or screws.
Screws hold better, but stainless steel nails last longer. Why not use stainless steel screws? They're the best of both worlds.
Neither use adhesive