Gatorskin Wirebead vs Folding (Which gives a smoother ride)
Folding bead alone will not affect your ride in a notable manner.
Here are some things which will affect the ride a lot more than whether it's folding or wire bead:

Tyre width (bigger = smoother)
Tyre pressure (lower = smoother)
Rim width (wider = smoother)

The difference between folding and wire beads are not really about comfort.
You could argue that the sides of a folding bead tyre are a bit softer than one with a wire bead, so if the tyres are the same or similar price, go for folding. Personally, I have not noticed the difference between my folding and wire Gatorskins.