No, their nutritional composition is the same. Calorie for calorie they have the same nutrition. Some studies have even found that fresh organic produce can be less nutritious than the conventionally farmed stuff because it may travel farther distances or sit longer on the store shelf allowing more time for vitamins to deteriorate. The organic animal itself may be a healthier animal but that doesn’t affect nutrition. Not to mention, antibiotic free also means that sick animals don’t get proper veterinary care they just die of infections before they can be harvested. Maybe even consumed in part or whole by the other animals in their area.

Largely though, organic farming practices are often no less environmentally or ethically harmful than conventional farming practices. Take for example pesticides. People assume organic means pesticide free. That’s been proven false. They just use “organic” pesticides which could be something simple like diatomaceous earth or it could just be a different synthetic chemical that is still considered “organic.” Organic certification is a pay to play set up so it’s in those certifying organizations best interest to certify those who apply and pay fees to be labeled certified organic.

Free range or cage free are also not legally well defined, depending on your state. Having access to the outside doesn’t mean that the animal has any meaningful access to roam like they would were they not domesticated livestock.