For the most part it's purely bragging rights. XLR connections when fully and correctly implemented can reduce noise and eliminate ground loops.
In some circumstances this can be huge, but for most of us it's minor.
Also, as others note, if you are using very long runs to other devices with truly balanced inputs this is helpful in ensuring there's no noise pickup along the way. Some devices, like some Parasound amps as an exmaple, have XLR inputs as convenience but they are not balanced inputs, so you don't get the benefit of a long run with less noise.