I think it depends on the meat and the veggies. I eat only free range, organic, hormone free, antibiotic free meat. Ditto for dairy and eggs. So, basically- no feedlots, no gross stuff in my food, humane life. By the way, I worked on ranches for nearly a year for my dissertation, and the cattle on western ranches really have good lives, even if the calves' lives are a bit short. So long as you avoid the feedlot, it's a great life and they pretty much just graze on wild plants. Good ranchers actually give benefits to the environment rather than harm, but the problem is who is good and who isn't, and the feedlot and packing system. I'm writing a book on it, hopefully to be published next year.
But suffice it to say, I've seen beef ranches, and I've seen dairies. The dairies are WAY worse. Unless you buy dairy products from one that has free range practices (pasture-fed cattle), the cows are kept in disgusting conditions. Same goes for chickens/eggs, and while white meat in chicken may be more healthy than fatty red meat, a lean steak is nearly comparable and you don't avoid all the nasty hormones and antibiotics unless you buy free range.
I don't eat nearly as much meat as the average American, though, because our average eating habits in the US are very unhealthy. We don't need that much protein. I eat meat nearly every day, but only as a garnish or flavoring. For example, I'll cook a stir-fry that is about a pound of veggies and brown rice, with just one chicken strip chopped up fine for flavoring, or a couple scrambled eggs, or a very small piece of beef. Or a pound of veggies and pasta in olive oil with about four pieces of bacon chopped fine. That way, my husband and I can get the taste of meat but without eating much of it.
Also, in terms of veggies and grains, unless these are produced organically, it's still contributing to major environmental damage. Pesticides, petroleum use, etc. Ick.
ETA: I totally agree with you about the mice and things Dauer. We lived in an old and unrenovated house for a while years back and had many cute tiny field mice. Some my cat would catch, and I always took them away because she'd play with them until they died more or less of fright. She never bit or clawed them, just carried them around and tossed them in the air. It was too sad to watch. Other times, she ignored them because she wasn't in the mood to play. We couldn't bear to set out traps or kill them. I'd just leave them alone. Of course, in our case we lived in a 30 acre field, and you just released them and back they came. I just kept all food in the fridge and all dishes in the cupboards. They'd still come in for water and warmth, but man, they were just so cute with their tiny black eyes and gray fur.