Both are the same grass hay plant, timothy, "Western" and "Eastern" simply specifies where in North America it's grown. Where they are grown does make a difference in quality of the hay, Western North America (more specifically Midwest where you see all the big farms) naturally has the best growing conditions including the most fertile soil, so the timothy grown there is going to be better quality in general, like containing more nutrients, better flavor, etc, making it the most ideal "best" timothy hay you can buy. Obviously you can get good quality hay in the east too if you add nutrients to the soil in the hay field, it's often more expensive though and normally advertised as premium "horse hay" or "horse quality" timothy hay. For chins though, since they also get pellets that contain the nutrients they need, there really isn't enough of a difference to matter, whichever your chin will eat is the "best" for them.