Which branch of lawyer makes the most money?

It all depends on how good a lawyer you are, and what kind of clients you represent.
Government lawyers (prosecutors, public defenders, JAGs) are usually on the bottom of the pay scale. They get great benefits and a more stable work environment though, so it all evens out.

Private practice lawyers usually make more money, but their lives are usually a lot worse. Personal injury lawyers usually work on contingency, meaning they get paid a fraction of the settlement or the jury awarded damages. So their paycheck depends on what kind of cases they try.

Consider a personal injury attorney whose client's wife was killed by a drunk driver. The client is suing for wrongful death of her husband. The jury is likely to give the client MILLIONS of dollars, and the lawyer takes a cut of that. But, during the time he is trying the case, he has no family life, no free time, no time to eat or sleep because he is conducting depositions, interviewing and preparing witnesses etc. And if he loses the trial and is working on a contingency basis, he gets NOTHING.

So, long story short, it all depends. Corporate lawyers make a lot of money too. Think of all the money BP is going to spend on lawyers to help defend them from lawsuits from the gulf oil spill. Think of the amount of lawyers working for tobacco companies. I would say that corporate lawyers make the most money.