Dungeon Buff Edit
A Dungeon Bonus is applicable for the Weekly and Daily Events (on Android).
The Buff is a bonus percentage on ATK, HP, and XP ranging from 0% to 30%. The buff increases by 2% whenever one of your friends enter such a dungeon. By tapping Enlist a Friend you can notify a friend that you would like him to enter a specific dungeon.
Element Affinity Edit
Each dungeon has a primary element, meaning most of the monsters inside are of that element.
Attacking a monster with a stronger element gives you a bonus of x1.3 on ATK.
When attacking with a weaker element, you lose a factor 1.3 on ATK.
When you attack a Fire monster with Water, and you do 1,000 points of damage, you will actually do 1,300 points of damage.
And when you attack a Fire monster with Wood for 1,000 damage, the actual damage will be 1,000 / 1.3 = 769.
Chance on Rewards Edit
The rewards are proportional to the amount of energy spent.
For instance, in the daily event for the Keeper of the Knowledge, you'll get about 1.5 more keepers on Hard than you would get on Normal, which matches the energy cost of 30 against 20.
Furthermore, the higher difficulty brings in higher chances on rares at the cost of uncommons.
This shows in the fact that Extreme in the daily event for the Keeper of Knowledge effectively lowers the chance on the uncommon keeper, since you'll get rares.
Last but not least, the chance of an ultra rare (a god) in an extreme weekly event, is about 2%. Presumably, the same chance in a hard dungeon would be about 3/4 x 2% = 1.5 %.