I know that it takes more damage to kill enemies, but apart from that is there any more experience gained on the higher difficulty levels?
Well, yes, and no.
On it's own, altering the difficulty does not affect skill gain rates.
What it does affect is damage done and received, which adjusts the rate it takes to learn offensive and defensive skills.
If an enemy has 300 health on normal and 300 health on master, though it might take longer to defeat him on master, you'll earn the same amount of experience for inflicting 300 damage at the end of the fight.
Leveling is base on how many time you successfully use the skill. So for instance, you need to successfully land attack 30 times to level a skill. In Novice, you kill a creature by hitting it 2 times, then you need to kill 15 times of the same creature to level. In Master, you need to hit a creature 10 times to kill it, then you need to kill the same type of creature 3 times to level.