Almost no character would be added unless you used a ton of them. Their flavor is subtle (light berry maybe) plus a "green" plant character from the outer skin. I don't think fresh figs are the best way to get "fig" into a beer - dried are probably a better choice to avoid the plant character and get the most from their subtle character.
Yes, dried figs give what would be expected as fig character in a holiday ale, quad, etc.
That being said if you have a real lot of fresh figs you might be able to coax a subtle flavor out of them. I would cut off the skin and pith and just add the reddish flesh and lots of it after primary is about finished. It might compliment a citrusy pale ale. I would only bother if I had a ton of free fresh figs.