I really like the ambient game music, and it's usually what I listen to when I'm out exploring or questing. Listening to other music while exploring just doesn't seem 'right' to me. I also really like Diamond City Radio though. I have multiple radios in all of my settlements playing it, and a lot of the time when I'm building I'll turn it on in my Pip-boy. I do feel like it gets repetitive though. I love the songs, but I wish there were more of them.
I just recently installed the Cadillac Jack's Radio Shack mod, which is part of the Old World Radio - Boston series of radio station mods. Currently it's a replacer for the classical station, but will become a standalone eventually. This station is great. It has all of the songs from Diamond City Radio, plus an additional 60 songs that follow the same general theme. It's very lore appropriate, and it's also professionally voice acted. It has commercials for Sugar Bombs, Wonderglue, Nuka Cola, and all kinds of other 'name brand' items that you find throughout the world. The announcer is incredibly well acted and has some comical dialog.
For anyone that likes Diamond City Radio but wishes it had more songs, I can't recommend this mod highly enough. It's just great.
And I just looked and apparently there is now a standalone version of it! Excellent. Looks like I have a mod to update.
http://www.nexusmods.com/fallout4/mods/5475/?