Another Swiss band i have encountered by accident. Hillbilly Moon Explosion. They are based in Zurich. It's hard to get a grasp of them just by listening to a few songs. Because their style covers several genres. They're not wildly famous, though, it seems and still would have to be classified as underground as far as I can tell. I like this cover of "Call Me" better than the original. Of course I was never a Blondie fan, although I always thought they were okay. The HME lead singer is Italian-Swiss, BTW.
After watching the band's videos a little more, I thought there is one thing I need to add. Sometimes they have a guest vocalist with a very gruff and deep voice. Exactly why they choose to do this, I really don't know. I don't think it adds anything to the music. But he isn't part of the actual band. To me it ends up being a little quirky, but I think it's safe to say a number of rockabilly bands are quirky. Wikipedia describes HME as European rockabilly with a mix of rock and roll, jump blues, roots rock, surf music elements, etc. They've been around for a while. They opened for Jeff Beck in 2010, one of the earliest references I've seen. I'm just giving info I've run across. Personally, I seriously doubt I would even be able to adequately explain the difference between psychobilly and rockabilly.