Not directly I think. But in f2p you can only do the first 35 floors, so your XP will be a shitload less than a P2p player, who can access all 60 floors (higher floor=higher exp).
On members you get more xp because you have more floors, more rooms (on f2p there are rooms for members and cannot be opened), better weapons to kill monsters faster, better food, better runes etc etc.
F2P can do 1-35 weapons, and only get to tier 5 objects.
(http://runescape.wikia.com/wiki/Dungeoneering/Equipment#Melee)
As well, members puzzles may appear in F2P, they can not be completed.
Finally F2P Players above 90 combat take a 50% xp reduction.