For me the two are very similar. I work in an open plan office and enjoy being able to talk to my co-workers - often someone will pull their chair up to someone else's to pair program for a while, or just discuss the issue they're having.
If you don't want interruptions, you put headphones on. It works well.
It works well for some people. While you may be able to code perfectly well with music blasting in your ears (loud enough to drown out nearby conversations) that is not the case for everyone.
I wear headphones at work but the volume (at which I can actually concentrate on my work) is only sufficient to drown out/filter random background noises (typing/mouse-clicks, HVAC, people walking by, etc) - if there are people having a conversation a few feet away my productivity plummets.
Headphones may be at best a distraction mitigation, but what they really are is evidence that your environment is crap.