Grass-fed/ finished beef is worth the cost because it is actually safer for you to eat. Cows that are fed grain, corn or other foodstuffs develop severe digestive issues. Their bodies are not designed to eat such things and it causes an imbalance of bacteria. This can cause infections such as E-Coli. The bacteria can be passed on to the consumer or the bacteria is fought with antibiotics which is passed on to the consumer. Either way, the meat is contaminated.
Not to mention, cattle coming from feed-lots are given hormones, antibiotics and other medications to fight diseases passed along because of small, dirty living conditions. Cattle who are raised on pure grass in their natural environment produce safer beef for us to eat.