I'm imagining that you are comparing low quality (grass only) hay to alfalfa hay. I have cows and horses. My hay guy is a cow person and feeds them alfalfa cause he's seriously trying to improve production etc. This is not the case with horses. Alfalfa can cause you all kinds of problems with horses and lesser hay is better, believe it or not. A horse should not have more that 1/3 of his diet in alfalfa, the rest should be grasses. Why? Colic is the first concern. YOU DON'T WANT THAT TO HAPPEN. Graduating to the new hay slowly over 7-10 days also helps to creat the new organisms needed for the horse to digest it, otherwise it will go right thru him. This factor is the same with cows as well. The difference between the horses and cows is that cows can burp, horses can't. If they get an upset tummy, they have to push it thru and that takes time and you've got colic, which with any imbalance such as this will go straight to the legs and the horse will founder, if badly, will rotate the coffin bone in their hooves and you have nothing but a horse in tremendous pain and expensive farrier bills and never get to ride again. No, you don't want colic.
Hay is EVERYTHING. If you are not feeding grain, then it's 100% of your horse's diet and that's pretty important. If he's eating grain, which he doesn't really need to at this time of year then hay is 70% of your horse's daily diet. Get it tested and know what's in it...that's the only way.
Horses need a calcium/phosphorus balance as well, they require less protein than a cow in production. With normal grass hay, the Cal/phos balance will be 1.5 to 1. which is best...critical if they are still growing. The protein is sufficient for horses on grass hay as well. With alfalfa, the protein in higher, creates a hotter and harder to manage horse and the cal/phos. balance is really high in cal. and really low in phos and can produce readings like 3/1 or even as high as 7/1, which is not good. Adult horses can be tolerant of these extremes, but with a growing baby, you are really bucking for epiphisitis in the joints (inflammation that causes deformities, in short)
My neighbour, who produces a lot of alfalfa told me of this lesser field of grass hay that he has and I went and tested it and it passed, so now even though its his field, its my hay and I get the hay off that field every year. I still introduce the new hay very gradually, though. Can cause problems with colic simply because its so fresh off the field etc.
Other guidelines that I use are to water down the hay well before feeding it......religeously. One bad dusty meal and the horse will suffer from a depreciating lung disease called Heaves that progresses in the horse gasping for air to the point where he just can't breathe anymore and you have to put him down. (A slow downhill slide that takes about 2 years) Another insidious preventable problem. I had a equine nutritionist tell me once that when it comes to feeding horses, less is better and I believe it. From the way that they look all the time, I know that they are in excellent health from the inside out. I operate on a shoestring budget and could never afford to jump on any supplement band wagon. I only give them vitamins in January, because most of the Vit. A has gone from my stored hay about then. When I think of better quality hay, I think of healthier hay, not hotter hay. Hope this information helps!