Seriously, I haven't found a genre that the TBird doesn't work will with. For blues rock I'd probably lean towards the TBird with flat wounds or possibly Black Beauties or Silver Stars. It'll sound a bit less aggressive and more P bass like with those strings.
I've only been playing TBirds for a couple of years now, but I can honestly say that since I got my first bird I really haven't played my P basses much at all, and I almost never play my Jazz basses anymore. I think @dukeorock is having similar experiences. The biggest hurdle is getting bandmates to listen with their ears. The audience doesn't seem to mind either way. My drummer was the first to yell "hell yes" after just a minute into a song in practice. After that the guitarist and singer were equally impressed with the sound, but I gotta be honest, it raised a few eyebrows in practice when I first pulled it out of the case.