Large chests are bigger than the smaller ones so they are able to carry more loot; these chests begin to appear at the fourth level of the dungeon and carries anything from Gold to Legendary weapons.
Mimics are disguised as a large chest before you engage them. There is a way to tell a normal chest from a Mimic, as there is always a swivel or streak of white magic around a chest from time to time, and a Mimic always has a faint purple glow underneath them.
A large chest can carry (at the most) three different items. Mostly these chests carry small weapons but you can also obtain a good bit a gold from them as well. Your chances to find gold in a chest gets larger as your luck increases and if you have a weapon or suit of armor that has a 4% rare drop which will either make the chest have a legendary weapon inside it, or a great sum of gold (100 pieces or more).