When you are looking at different hays (or "forage") for consumption by your rabbits, keep in mind that you don't need to be as concerned with the nutritive values as you do with other foods. Rabbits are primarily grazing animals. Native grasses and plants being their normal diet. It's when you start adding in items and amounts they wouldn't normally get in the wild, that's when the nutritive value becomes important.
Alfalfa for example is a legume, not a grass. It is very high in Calcium. Good dried Alfalfa has as much Calcium, pound for pound, as dried milk! Obviously, that's too high to be used as a dietary basis for animals like rabbits, who tend to excrete excess dietary calcium through their urine instead of their feces (like us). It means they are more susceptible to blockages from the excess calcium.
Timothy hay is named that because Timothy Grass is the major component in it. There may be other plants, that have grown up in the field, but Timothy is the main ingredient.
The USDA does not recognize "Western Cut" as any different from any other. I would guess that it is just hay from the somewhere out west, that has a few different indigenous plants mixed in with it. I would suspect it is more of a marketing ploy than any substantial difference. Any good grass hay should work well for rabbits: Orchard grass, Timothy, Brome, etc.
Some of the things you want to look at when examining different types of forage are: Dry Matter (DM), Crude Protein (CP), Acid Detergent Fiber (ADF) and Neutral Detergent Fiber (NDF).
Here is a PDF file on Interpreting Hay Analysis
, that explains what these terms mean, and how they affect the quality of the forage.
Here is some nutritional data on various types of forage:Hay Buying Guide
Where you buy your hay shouldn't matter as long as it is relatively fresh and free of contaminants. I have always found it more economical to buy a whole bale from a local farmer. It is a tiny fraction of the cost of storebought, and if kept in a dry dark place (in my garage on a wooden pallet) it keeps for a long time (months).