The title says it all. Both have the ability to switch between melee and ranged, although nid requires lvl 6 to do so. Damage wise, Jayce is pretty much the superior dealer since he can just jump in and whack the opponent around while Nidalee's melee is generally used to finish off opponents. However, I do think Nidalee provides way better utility and can provide any role the team requires....except being a tank whereas Jayce is generally an AD carry.

So ignoring team compositions, who would you pick?

nid. dat in lane healing.