I actually don't agree with the current, chosen answer.
The Why of It
"Be the mouth of a male-chicken than the tail of an ox", to me, means this:
Strive to be a leader, heard and respected by others, instead of being a forgotten, unimportant person
A male-chicken (that is, a cock, but I'd rather not refer to it as a cock) screams loudly every morning; everyone heeds the screams of a male-chicken, for it means a new day has come and everyone gets up from their bed; the tail of an ox is pretty much forgotten until it causes trouble
What Others Are Saying
I am simply telling my interpretations here:
Better to be a big fish in a little pond than a little fish in a big pond.
This actually means you should find worse people to hang around with instead of bettering yourself. For example, if your academic scores are average, you should go to a lower-ranking school filled with less-knowledgable students to make your scores relatively good. While this does carry a similar outcome (that is, you're seen as a leader instead of falling behind), this carries a negative meaning. Another interpretation would be that you should find a range you're comfortable with, but it's just a sugar-coating
Better to reign in Hell, than serve in Heaven.
This simply means that you should find a job you're happy with. Seriously, think about it: Satan didn't like having to do what God (his boss) told him to (serve in Heaven), so in spite he found a job he'd rather have: reign in Hell. When you strip out all the religious symbols, the meaning becomes simple and is actually pretty positive.
The closest one that I think should be the answer is @Josh61's
Better to be a leader than a follower
I just feel that the tail of an ox does not imply a "follower", instead more like an unimportant person