(1) What are the best full frame bodies for high ISO these days?

(2) Is the difference significant?

My 5D II shutter blew the other day and I need to replace it. The obvious thing is to get a 5D III (or one of its variants) but before I do, these questions would be useful to have answers to. I use the 5D II for a variety of tasks and I probably wouldn't switch camps just for high ISO work, but one of the things I loved about it was its amazing ability to produce good clean shots at silly light levels. I understand that more modern cameras are (amazingly!) even better again, but I haven't been following the latest models for quite a while now and am out of touch.

Is there a huge difference between the main brands and models as regards high ISO work? If it isn't all that much, it would be most convenient to stay with Canon. But if the difference is big enough, I am not averse to sneaking an other-brand cuckoo into my all-Canon nest. (As per sig I use multiple bodies; if I added an other-brand camera I'd only get one, at most two lenses for it. A 24-70 or something similar.)

Thanks for all responses!