From the perspective of an old farm kid who used to raise hogs and cattle, animal husbandry major, with some meat science training, I'm in agreement with Reinman.
Prime beef is the primo stuff, and is generally going to come from young animals with the right genetics (primarily black Angus), which are given some grain during all growth stages, but are finished on a near total grain diet in a dry lot for the last month or two before slaughter. Tender comes from genetics and being young, flavor from the marbled fat in the muscle.
Then, to properly finish them off, after slaughter, a carcass is covered with a shroud and hung and aged in a cooler for at least a week or maybe two before it's cut up and processed. Aging gives the meat a distinctive flavor and also allows time for the connective tissue to start breaking down on it's own. Aging enhances both flavor and texture.
Some locker plants will send a truck to your farm, drop the animal in the pasture where he stands (no stress) and start the processing there. That's as good as it's going to get.
By comparison, grocery store beef is coming from who knows what, but almost certainly from a fast growing crossbreed of some type, will have some grain, but depending on genetics, will never finish off properly. Steers with dairy blood in them will just keep growing and you play hell getting them to fatten up. You find that stuff in cheap, chain style steak houses and likely as not, they have had chemical tenderizers added so you can chew them.
As for processing, the store bought animal probably had to ride on a truck for at least a day, hit the slaughter plant (adding stress the whole time....read tough meat), and is parted out into boxes and shipped the same day.
So there is a reason for one being better, but grass fed isn't the most important. In fact, in my book, that's setback if a tender, juicy, flavorful piece of meat is the goal.