Grass or grain: it's a simpler-sounding question than it is.
Grain feeding isn't the villain it's sometimes made out to be; the animals aren't mistreated, and there are legitimate reasons it's used.
What it does is change the composition and flavour of the fat. Grain-finished carcases also tend to be more consistently finished, which helps tenderness; grass-fed beef can match that, but only when the animal is well managed and well finished, and that's not always the case.
An animal's diet also changes the nutritional value of the beef, not just the flavour.
Grass-fed beef carries more omega-3 fatty acids, vitamin E and beta-carotene than grain-finished beef and has a better omega-6 to omega-3 ratio.
It is also richer in pentadecanoic acid (C15) and margaric acid (C17), two fatty acids with a growing body of claimed health benefits.
Grass-fed beef also has two to three times more Conjugated Linoleic Acid (CLA) than grain-fed beef. CLA has been shown to improve metabolic health in some studies.