Cooking meat is all about getting the internal temperature hot enough that it is “cooked” without drying out the edges. For grass fed beef, success comes when you turn the heat down. Grass fed beef is naturally leaner. Your conventional beef has more fat, thus more insulation. Therefore, higher temperatures are necessary to penetrate the meat. When in doubt, turn it down, and have patience.
Given the variability of cuts, the only true way to tell if it is “done” is with a meat thermometer. For roasts, this is an essential item. Place the thermometer deep in the cut, away from bones and the bottom of the pan. The USDA recommends 140-170F, but I think that is too high. Follow the government recommendation and you will consistently have a dry, tough dinner. Harold McGee, author of On Food and Cooking, recommends 120F (rare) to 140F (medium) to 160F (well). I would personally stay on the lower end of that scale to experience beef at its best!