I don't work in this field, but here's an educated guess (or two).

Lasers are not perfectly coherent, parallel beams. They're close but, over the distance between the Earth and the moon, even the most powerful, carefully adjusted and perfectly focused laser will expand much like a flashlight beam. Take the laser pointer you use for presentations and shine it across the room and you'll see a substantially larger spot size than if you shine it on your hand. You get the idea. Getting a strong signal means you need a lot of area in your receiver. A big dish will help at either end, but it's harder to send a big dish to the moon.

Another huge factor is going to be atmospheric distortion. The atmosphere is full of eddies and currents of air at different temperatures and relative motions. Light going through it gets refracted somewhat chaotically. If you try to lock a free-space laser signal in over a distance of even just a few tens of kilometers through air, it's actually a bit of a challenge because that (rather large) spot will jump all over the place. Light traveling from the Earth to the moon goes through atmosphere at the source and gets bent and, by the time it reaches the moon, will be all over the place. Light traveling the other way travels through vacuum until it's very close to its destination. Consider trying to shine a laser pointer up out of a pool of choppy water and hit a distant target vs trying to hit a specific spot in the pool from that target. It's a lot easier if the random bending happens nearer to the destination! There are a lot of things you can do to overcome this, but they probably all reduce the speed at which you can transmit.

Edit: I just read this: http://www.spaceflight101.com/ladee-lunar-laser-communicatio...

The sending and receiving modes are completely different. The moon craft sends polarization encoded data using a continuous beam. This is received on the ground by highly sensitive single-photon-detectors hooked up to multiple large scopes. Sensitive, but bulky and components have to be cryo-cooled. However, this allows for the use of a relatively weak laser at the moon and polarization modulation means you can probably get pretty good bandwidth, provided the atmosphere isn't so turbulent that it requires you to check your states too often. (Polarization will be randomly transformed by the atmosphere, so you'd determine which polarization is which periodically as a part of communications. This is presumably why they have multiple receivers that are probably measuring in different bases so each bit from the moon can be tomographically reconstructed.)

The ground-station sends pulse-position modulated (aka time-bin) encoded data with a fairly powerful laser. Say you wanted to signal a friend yes or no without talking. You could synchronize a pair of stop-watches and, at an agreed time, you throw a ping-pong ball at his head. If you want to say yes, you throw it right on time. If you wan to say no, you throw it a bit late. Obviously, your ability to distinguish early from late limits how fast you can send data this way. If it was a windy day with random gusts, the ping-pong ball would arrive a bit randomly, so you'd need to make the delay required to declare a ball "late" somewhat longer. Atmospheric distortion probably limits bandwidth to the moon for this reason.

Both polarization and time-bin encoding can be made to work both ways I suspect, but there might be reasons to choose one over the other for sending vs receiving. It does seem like the receiving station for a polarization encoded signal might be more bulky due to requiring multiple detectors operating on different polarization bases. I'd love to ask the folks at NASA about this! It might also be they just wanted to test both methods, since this really is an experiment more than anything.