Hay can really vary in the richness of color– many people think that because hay may not be really green, that it is not fresh or good. That is definitely not the case. Brown can happen for many reasons, (weather, how the hay leans while growing, the timing of the harvest, storage,etc), yet it can still be fresh and good for your bunny. As long as it is not dark dark brown and smells fresh then the main thing that is in tact is the fiber. Water damage can make hay darker, but you just have to be sure that it’s not mold (which will have a musty smell to it)
Nutrients are a little bit higher in green hay, but bunnies don’t get most of their nutrients from hay anyway—it’s all about the fiber when it comes to hay.
I have heard that hay for cows does differ in quality than what is typically given to horses, rabbits and smaller hay critters. I know that one of my own hay suppliers has a different quality of hay for cows, than they do for horses, rabbit, guinea pigs, etc) I really am not sure why that is, maybe the digestive differences somehow? I’ll have to look more into that and ask specifics.