You can drop loot on another character's portrait to transfer it to their inventory, or drop it for them to pick up.
There are no classes, so no class specific loot (though of course there will be equipment that doesn't fit with your character build). In co-op mode I think most people are going to want to try different builds, so equipment shouldn't be much of a problem. I suppose one person could gab most of the potions, etc, but if the combat is balanced for 2 characters they are going to start running into trouble if their greed ends up handicapping the other player (assuming their behaviour doesn't outright discourage others from playing with them).
Also, there is friendly fire in the game. You can always 'accidentally' hit someone with a fireball, and then say "oops, sorry, I was just distracted thinking about that 4th time you grabbed loot in a row and didn't give me anything."
What if they both planned to go on the same stat allocation, same build and whatnot. I don't know if it is possible to make the game doable with this build but there are instances where people try this route.
I personally agree with the above poster about the "everyone can see my loot", the equal sharing of gold, and possibly, the equal loot distribution.
Have it as an option before starting the game. Let's think pessimistically and assume that all men are greedy. This would make the coop an unfriendly option.
Since the other player can be far away from the other one, the above mechanic is unforgiving for those who takes quests and gold a lot. So, a good control is to limit the distance the other character can get the loot/gold. Basically, what other online games are doing. It kind of ruins immersion, but it makes the game convenient/practical.