食う isn't vulgar at all. I would say it's more "rough" than 食べる, so it's mostly only used by guys. Not an exact correlation, but English has many words analogous to this: chow down, scarf, munch on, dig in, etc.

Yeah, it's not vulgar to the extreme that we might think when we hear the term "vulgar." But it is much more informal than 食べる。

For example, if you asked your friends mom whether she had eaten or not by saying, 「飯食った？」the mother would certainly get a strange opinion of you. That either you were a rude kid, or just not smart enough to know that 食う is not something you say to your elders.

However, among friends, especially men, the phrase 飯食った？ Or なんか食う？ Is used -all the time.-

In addition to the former answers I would add following things. 食べる used be a humble form of 食う but lost its original humbleness and became just to mean 'to eat' and now it replaces many usage of　食う. But 食う still has more usages than 食べる. For example 蚊に食われる, 時間を食う or 人を食った言い方 etc.　can not be replaced by 食べる.