That commonality doesn't seem sufficient (to me, a non-expert) to show that there is no difference in meat nutrition.

It definitely makes a difference, cows gain a lot of fat on a grain diet. The original reason people did this was the meat tasted better, but we’re extending that time period because subsidized grains are so cheap.

Omega fatty acids profiles of leafs and grains are entirely different. That ratio directly translates into the composition of cellular membranes of cows and eventually humans who eat them. Plus there are very different vitamin composition and even amino acids ratios are different.