More Nutrition in Grass-Fed Beef
Grain- and grass-fed beef both provide important health-boosting nutrients like vitamins B12, B3, B6, C, and K2, as well as selenium, zinc, and iron.  Beef of any kind contains carnosine, creatine, and high-quality protein, which is crucial for your brain and for building muscle.
The winner on the nutrition front is grass-fed or grass-finished beef, which is higher in certain nutrients, such as:
Vitamin E: An important vitamin for reproduction and vision health and an antioxidant that protects cells from oxidation.
Vitamin A: Grass-fed beef provides carotenoid precursors to vitamin A, including beta carotene, which is known to protect vision. Remember vitamins A, D, E, and K are fat-soluble and largely stored in the fat of the animal.
Antioxidants: Grass-fed beef usually provides more antioxidants. 
Different Effects on the Environment
Cattle that graze and roam freely can increase the carbon-carrying capacity of the soil and restore crucial nutrients to depleted soil. Properly raised cows have a minimal negative effect on the environment and can actually improve the environment.
Proponents of grass-fed beef point out that monoculture crops, such as corn and soybeans grown to feed grain-fed cattle, destroy topsoil and increase greenhouse gasses in the atmosphere. On the other hand, they believe naturally grazed cattle can help the soil sequester more carbon and offset greenhouse gas emissions. In other words, eating natural grass-fed organic beef and supporting regenerative agriculture can actually assist in reducing carbon in the atmosphere.
Regenerative agriculture is backed by decades of research and designed to mimic nature with the goal of rebuilding organic matter and healthy soils and restoring degraded soil biodiversity, fertility, and nutrient density. This way of agriculture also increases water retention and promotes cleaner and safer water runoff, as well as boosting local economies with family farming and preserving traditional indigenous farming practices. Locally grown produce also generally has a lower carbon footprint. 
What About Organic?