Romans 14 as a whole doesn't endorse a vegetarian diet as necessary or otherwise better. Look at the beginning of the chapter for the context:
Romans 14:1-4 (KJV)
1 Him that is weak in the faith receive ye, but not to doubtful
2 For one believeth that he may eat all things: another, who is weak,
3 Let not him that eateth despise him that eateth not; and let not him
which eateth not judge him that eateth: for God hath received him.
4 Who art thou that judgest another man's servant? to his own master
he standeth or falleth. Yea, he shall be holden up: for God is able to
make him stand.
What Paul is saying is that some believe it is better not to eat meat, and that if he is in such a case as to be a cause of temptation for such a brother, he would rather not eat meat at all so that his brother is not tempted. This is the same problem as wine in a way, in that wine is not bad in itself, but it is better to not drink wine if it will cause a brother or sister to stumble.
Paul is not saying that it is better to be a vegetarian, but he is warning to not let such fleshy matters be reasons for brothers or sisters to stumble. In other words, I'd say if you are eating with someone who believes being a vegetarian is better, don't argue on it, just go with it so it doesn't become a subject of stumble for this brother or sister.