Ahhh, interesting. I see where you're coming from. There's one song that comes to mind in particular that I love on YouTube, but dislike when it plays on the radio. On YouTube it's just the artist, his guitar, and some drums, where on the radio it sounds a bit loud and overwhelming. Is there a particular country/bluegrass song you have in mind? I never listen to country music, so I'm interested in it!
For country and music of that ilk, I'd first recommend you try out Justin Townes Earl. "They Killed John Henry" is probably my most favorite song of his, partially because it sounds so good and partially because it's about worker's rights. While his style has changed over the years, he's very accessible. A lot of his songs are about personal matters so he always sings from the heart. Not all songs are down and somber. The Devil Makes Three -Spinning Like a Top is nice and upbeat. I will admit that some music does not translate well to live sets and that tends to be songs that are both busier and faster. So while I can't find a decent live version of it, I can't help but share Wait so Long by Trampled by Turtles. It's just a fun, frantic, well put together piece.