Real simple: YES. Anything that is an animal product, always, always go organic. This means there are no pesticides, hormones or additives to the animal's life, and that they were kept in a humane manner, allowed sufficient pasturage to roam in the case of cows, goats, sheep etc., and in the case of chickens that they were not cooped and allowed to scratch freely and have room to stretch their wings. Also, that they were killed humanely and treated with dignity throughout their life and in their final hours. It makes a difference in the taste and nutritional value of meat, milk and eggs of domestic food animals, plus which it's just the right thing to do for all the reasons above.
Put it this way: Would you eat a piece of chicken pumped not only full of artificial hormones and antibiotics, but the extreme stress hormones from being cooped beak to beak with other birds all its life, who suffered before dying and was killed inhumanely while terrified? I know I wouldn't. My conscience won't let me, and my body, fed for over a decade now on organics, knows the difference. Organics are also one of the best ways, animal or vegetable, to cleanse your body of all the poisons you've ingested over the years.
Dark Knight speaks of organic farms not producing what pesticided farms do. That may be true, but would you rather eat poison or quality nutrition? It's also over 100 years of using pesticides and other chemicals that have leached the core nutrients from our soils such that we have to supplement them by taking vitamins - even with organics. Those farms that have been organic 20 or more years have put back the nutrients into the soil. Food from these farms is more nutritious, and if you feed on it, your body needs less food to live better. Part of the overeating we're seeing as pandemic right now is caused by the very poor nutrition available even in plain meat and vegetables that are produced on chemically saturated lands. The body is just trying to get its RDA of nutrition, so the person eats and eats. It's a shame the available calories in such food haven't gone down too, or we might be able to break even. But that's not the case... *wry smile*
Also, in turning our lifestyles around from the endless consumption that factory farming is part of, we can leverage other options for food production. Rooftop and back yard gardens - in the 1940's during WWII, everyone had them and everyone fed their families nearly 100% with them. Farming the seas as well is technology we are only starting to leverage, unlike seafaring nations like the Scandinavian countries and Japan, whose bulk of protein comes from the sea. Hydroponics and community farms are also extremely viable options, even for city dwellers. In England, each family without back yard space for a garden may request an allotment of land from the city for the purpose of growing their own vegetables and keeping small livestock.
We might well take advantage of these options no matter what city, state, nation or principality we live in. It's no longer an east /west issue, or a north / south divide. Food and water are becoming scarcer, but that doesn't mean the trend has to continue. If we all pitch in towards sustainable longterm solutions, we can still turn back the tide of damage a century of chemicalized living has done.
Hope this helps! :-)