Like music in both as they fit their respective settings. I only wish Eden, Three-Dog and Mr. New Vegas talked a bit less.
Granted, I only listen to music while in cities. In Wasteland and dungeons, I prefer the sweet tone of ambient music
I don't see it as having anything to do with Beth: the NV hero is supposed to be a hero of faction X (and only one of many: supposedly many couriers are that badass in the West Coast so he ain't even that special) while F3's protagonist is supposed to be the Messiah who ended the Dark Age of Capital Wasteland (the game starting with a Bible verse and originally the ending with martyrdom should have made that clear). As such I'd say both DJ's fit their respective stories.