With mass-produced factory meat, there's honestly no difference.
The gist I got from trek, even TOS, was that it was all made on the ship. They wouldn't say no to butchered meat if offered, but the ship had great recycling systems and synthesis and it came out fat and all. Bone might not be an option, however.... But Kirk could probably had all the chicken sandwiches and coffee he wanted on plates of bejeweled gold.
A post nuclear humanity will suffer a glut of meat, no question there. Our factory production cannot survive a nuclear war, and most people will be grateful for a monthly or quarterly chicken on top of year old grain bread. But we're on track to have electrified urban farming and at least batches of semi-regular grown meat, and I would imagine ww3 would also inspire a bigger survivalist and home-gardening/homesteading movement just to have those chickens around until the governments got enough of a handle on things to restart bigger scale food production.... By the 2100 era, 260, the implication was, again, you'll have to go out of your way to find something raised and butchered than grown in 1000 tonne vats.