Hi Scott-- a fair question, but in response, I have to say that I don't care for jazz at all and have no explanation for that-- yet I know you're a big jazz fan? I guess we're wired differently.
First of all, there is no accounting for taste(s). That said, I find Margo Timmin's voice at once haunting and intimate on many of their (especially) ballads. Of the other band members, Michael Timmins, guitarist and writer is of near genius caliber, IMO. His "chops" are unusual but great in his unique way.
I have been a fan of Junkies music for years, but when I first heard them I wasn't, so Tim's right-- their music grows on some-- it certainly did me. Also I find it fascinating that it is not possible to readily classify or pigeon-hole their music. I mean what kind of music is it? folk? pop? country? blues? Well IMO, It's none of those yet it has elements of all of them and some others too. And their band work can be incredible-- one guy, not a Timmins-- plays something like 5 different instruments.
I can wrap myself up in the music of "The Trinity Session" and "The Caution Horses" , and relax in it too. Also, I find the lyrics on many of the songs inviting and with much truth about everyday events and truths-- and if that makes it boring, well, it's not too me. I could write a lot more about the Cowboy Junkies music but that's pretty much the essence of my interest. I think Dekay's observations fit for me too-- at least as I understand them. Cheers. Craig