Grass fed is better for you because the cows on pasture have a different composition of fat (like that of wild game) than cows on grain (corn mostly).
The farming establishment has known about this for decades. I learned about it in agriculture school 30 years ago. Grain allows farmers or slaughterhouses to finish cattle (fatten them) using much lower quality pasture or no pasture at all.
Eastern farmers can finish cattle on pasture. The best grass fed beef is in the area of the Appalachian mountains.
Cow’s eat anything they can get their lips around especially free range or pasture. Ranch land changes throughout the year with the vegetation going through cycles. During the spring and summer months is the only time they’ll much a little grass the rest of the time it’s whats available with weed’s of various cooler weather species being predominate. During the deep winter they all hit the cactus patches here in Texas or start stripping lover hanging tree’s. When finishing cattle what you feed them is not as important as how you feed them. Cattle in a pasture feed at will, in a feedlot it’s when feed is put out and that’s where competitive feeding comes into play. Cows will eat every time the feed is put out even when not hungry due to their competitive nature. Kinda like raising show hog’s you always raise two or three to get them to eat more.