Individual preferences aside, is there a ''rule of thumb'' regarding handlebar width?
what are the advantages/disadvantages of wider vs. narrower

Mostly only in Drop Bars for Road racing.

For drop bars people usually recommend bars that are shoulder-width. Personally I find that too wide, I'm a big guy but I ride 38cm or at most 40cm bars. The steering feels tighter, it encourages you to steer with your hips rather than your hands.

I like bars that are a bit narrower too. One of my buddies says that with wide bars it's like welcoming the wind with open arms...i.e. not very aero. Part of it is style/trend. Years ago bars were narrower. Nowadays, wide seems to be more common. With mtbs, it's gotten absurd, IMO. It's mainly a matter of personal preference so think about it, maybe try a few widths, and see what you like. Remember, when you're on the tops, the distance between your hands is a lot less than when you're on the hoods or in the drops. Does this cause you any issues?