There are probably others here who can speak more authoritatively about this. Most of my knowledge has come over time – and I have been sort of skeptical or agnostic. But reading Franklin Steak I am more intrigued now about trying more grass fed meat (particularly beef).
On taste, grass fed is a richer, more “beefy,” taste – which some may not like. These are somewhat generalizations, but my understanding is that grain fed tends to have a less strong taste, and thus appeals to those who may not like strong beefy flavor. Some argue that this is a more natural flavor, and thus we should like it, as it is what meat used to taste like. I am not sure I would go that far. I think if you like the taste of grain-fed, then more power to you.
On health, grass fed beef (and by grass, what is really meant here is a mix of grass and other plant material) tends to be higher in nutrients that are beneficial to humans. I don’t have the book in front of me so can’t remember the different nutrients – some omegas, others. It is also healthier for the cows, and thus produces healthier, and thus tastier, meat. On the other side, grain-fed tend to be more susceptible to disease – thus leading to the use of hormones and antibiotics with grass fed beef.
On the animal welfare front, I think this is where things can overlap but are not necessary. So some feed grass pellets to cattle in closed pens and claim they are “grass fed.” These tend to be less nutritious and, some argue, less flavorful. It is obviously less pleasant for the cattle. Many of the more “pure” pasture grass-fed ranchers also tend to treat their animals well – the argument being that animals with less stress also produce better meat.
Environment is also better, but again this is not necessarily related. That is, those who are serious about grass fed and pasture tend to also be serious about environmental concerns – so there is a correlation between grass-fed and environmentally beneficial practices. But you could also have grass-fed beef ranches that could also be less careful about environmental practices.
It is all pretty fascinating – and with many such things one has to dig a bit deeper to figure out who is doing what, for what reason, and then assess the overall result. If you are really interested I would urge you to buy and read Franklin Steak – it is written in a very easy and accessible style, and covers raising cattle, butchering, and cooking. As someone who tends to be more interested in the cooking side, I am more interested in the ranching and butchering than I thought I would be!