Does Multiplayer improve loot or just increase the amount of enemies and loot drops from them?

It's generally understood that more people = better loot in general, but it seems like this is mostly due to more enemies appearing and more items dropped (IIRC in BL1 Crawmerax drops like 2x as much loot in two player vs one player).

So is Chest and Quest loot totally unaffected? Are actual item drops any better on average or are there just more of them? Do enemies even actually drop more items (especially bosses) or is the bonus only because there are more enemies?

Solution 1:

One of the rotating messages that appear when the game is starting encourages you to play coop. That message says that there is more loot and better loot.

Solution 2:

There's no way to tell without diving into the actual coding of the game (which I can't do since I'm on consoles) but from my experience yes, you do get better loot because more enemies+more drops=better loot and I've also found that chests do seem to give somewhat better results with more people playing together. I've definitely found more purples and e-tech weaponry when playing with four buddies than when farming alone. Bosses unfortunately don't seem to drop anything more often with four people, however.