There probably isn't so much a deal with being vegetarian, and being more "pious". People are at different steps along their pathway with God. Lay people of course wouldn't be aiming for the same thing as a monastic, for example, because both live different lives. In saying that, in some cases, there are more pious people amongst laymen! But in the end, we're all hoping for Christ's mercy and salvation.
Another reason why monastics probably don't eat meat is, as was read in "The Ladder of Divine Ascent" during Lent: "Satiety in food is the father of fornication; but affliction of the stomach is an agent of purity." - St. John Climacus.
Being full, or "comfortable" after you've eaten a big meal, no doubt including meat, can often then lead to other indulgences. Why, I say this? I know - I broke Lent and didn't just have meat, but then ended up having the cake and tea and eveything else on top of it. "Once you have one thing, why not pig out and go the whole hog, you say to yourself! Now, have you learnt your lesson?" this is exactly what my priest said to me during confession. Indulging takes your mind away from God. When you're hungry (like during Lent), you realise just how much God blesses us with the good things that we have. Not only that, but you strive for more godly things. You're mind is not so focused on things of the world that are not important.
Anyway, enough of my preaching. I'm not a vegetarian, but after doing Lent this year for the first time in my life, I would quite gladly give up meat for more spiritual blessings. (Unfortunately, my family doesn't see it quite the same way and believe I need meat to be healthy. To save disruption to my family, I eat what I'm given .. but, quietly knowing that one day, if I do become a monastic, I will be able to eat vegetarian to my heart's content.)