Grass-fed beef is typically leaner with less fat and marbeling and requires slightly different cooking methods. But for many reasons, grass-fed is better because cows raised and "finished" on grass rather than grain are usually treated more humanely (i.e., raised in pastures rather than concentrated feedlots). Also, while there is no proof that grass-fed is healthier for you, it does have a higher concentration of omega-3's, which are very good for you.
A really great book if you are interested in understanding the differences between grass-fed and grain-fed cows is The Omnivore's Dilemma by Michael Pollan. FWIW, my husband agrees with you that grass-fed beef doesn't taste good, but I think a lot of it has to do with the lack of information and education about how to cook it.