Grass fed beef is produced from cattle which are allowed to range-feed on grass rather than manufactured feeds. When cattle are fed corn rather than grass the animals digestive system is disturbed and in order to avoid bloat problems and disease the cattle must be given antibiotics.
One important note; just because beef is labeled "grass fed" it does not mean it wasn't raised in a feed lot rather than in a pasture. Look for pasture-raised, grass fed beef. See our beef buying guide.
It certainly does taste different and it could take some time to get used to if you've only eaten grain fed beef. Taste is difficult to describe but I can describe it as having a slightly "grassy" flavor. I was raised on grass fed beef (we lived on a cattle ranch) and I was used to the flavor. Years later when we left the ranch I started eating grain fed beef and I grew accustomed to that flavor. I finally purchased some grass fed beef and I immediately remembered the difference of what our own beef tasted like. I've read that some people describe it as "gamier" and perhaps it is. When I think gamey I think venison or duck; that's gamey.
Grass fed beef is considered to be more healthful to humans because typically the meat will have fewer residual antibiotics and higher amounts of CLA (conjugated linoleic acid) and omega 3 fatty acids. It also has slightly fewer calories.
Personally, I suggest you eat the best quality you can afford be it grass fed or grain fed. Consider cutting your consumption down and just eat less of a better quality beef that is treated as humanely as possible.
Grass fed beef is more expensive than grain fed beef. You can substitute one of these options: