Are you usually sitting down to listen to the radio? Or is it usually just on while you’re already doing something? I only ever listen to the radio when I’m driving and I think most radio listeners are just using it as a kind of auditory wallpaper while they’re working or driving or shopping. It’s a lot less demanding of your attention that way and in turn we tend to be a lot less demanding of it in terms of entertainment value or being strongly affected by it. It’s just on and that’s all it needs to be.
If you’re exhausted after listening to just music rather than the radio, I’d bet it’s because you’re really listening to it which is a more active process and more demanding or your attention. Your standards for what you get out of it are probably higher in that context as well so you may be more likely to tire quickly of it too both because it’s so intense but also because if it’s not particularly amazing you’ll likely want to stop sooner than if it was the radio with regular breaks between songs and something else going on occupying your attention the whole time.