This thread has turned into a thread about which art is the best, etc. In answer to that question, you can't really compare them...which is why everyone keeps bickering like little school girls. Each of them is applicable to different people, circumstances, body types, etc.
Anyway, to the main point: the fear of physical confrontation.
The truth is that guys WILL try you. It's part of life. You get tested in the workplace and on the street. If you're with a hot chick, guys may attempt to make comments, etc, especially when alcohol is involved.
The best solution is to watch where you step. You know how you stand against other guys. Don't put yourself in situations that can result in problems.
You need to watch your back too. Know the mindset of aggressors. Learn the body language, etc. that may indicate trouble can start. That you can evade the problem before it even arising.
Be prepared. That means that you feel secure not only about yourself but who you're with. Avoid confrontation AS MUCH AS POSSIBLE, but if it is unavoidable, you need to be able to take care of the situation as quickly and efficiently as possible.
FIGHTS ARE DIRTY. Don't think that martial arts gives you a cloak that will make you the undefeatable badasses. If you want to check out some real badasses, take a visit to a major city prison. Go the harder parts on the streets and talk to some of the thugs who have been in and out of the pen for years, where street fighting and brawling is a way of life.
There's two routes you can take. You can be that thug or you can decide that lifestyle isn't right and watch your step. But practicing jiu-jitsu for a couple years isn't going to make you unstoppable.
Real fights end with bottles on your head, head stomping, guns, knives, and bloody messes. They don't start in the ring and they don't have a ref.
Beyond this, know that you will be able to make a decision and ACT. If a guy has done something to you or your girl that you know deserves physical retaliation, you DO NOT THINK OR TALK ABOUT IT. You don't TALK. You don't throw bantering insults back and forth like little boys. Within a split second of the guy making a brash comment to him looking back to his pack of thugs, you've already clocked him to the floor. You ATTACK AND MOVE ON IMMEDIATELY.