They're often able to deliver a bit more power with fewer channels loaded, probably because most amps have a shared power supply and hence fewer channels loaded puts less stress on that power supply. If you had a multichannel amp that was basically a load of monoblocks then that is unlikely to apply unless you hit long term power supply limitations in pulling power out of the wall. Ultimately amps can be current limited and/or voltage limited and that will depend on the load being put on the amp. A one line spec rating isn't going to tell you much about this, serious amplifier tests are v rare though.
Power demands are actually really low most of the time btw so the performance in the first few watts is arguably much more important than the full power rating. For example I was testing a speaker I'm building the other day, it has pretty normal sensitivity (high 80s) and I had calibrated the amp to be outputting 2.83V (1W at 8 ohm), I then listened to some music for a while and it was a fair bit louder then I would normally play music at & probably about the sort of level I watch films at. Of course there are transient peaks that will burst above this but it's still a pretty low number, even a 20dB peak is only 100W on that basis.
As to sonic advantages, amps are usually rated for things like crosstalk so I suppose that might be a factor. You'd surely be better off spending more on an amp with fewer channels though.
