one advantage of AA/AAA batteries is that if you do lots of exotic arse end of nowhere holidays, you can probably still find somewhere that sells batteries, but a powerpoint that you have a plug for may be trickier. This is probably more relevant for cameras (not being able to listen to music is one thing, but not being able to take photos of said exotic arse end of nowhere is another matter), but I've started so I'll finish...
For normal everyday use, unless you need to listen for really long periods, I'd go for inbuilt rechargable every time. Of course, if you only have a usb charger (i.e. ipod), that is a lot less useful than a mains charger...