I would say the MK4 runs 6AS7-type tubes rather "gently". These tubes were designed to run at a significantly higher plate voltage than the MK4 can provide. And therefore, in your MK4, less than perfect tubes can often sound very good. On the other hand, your MK6, which is biasing them them properly, is running them "harder". And typically, tubes that are run hard tend to reveal their imperfections...
However, that said, the noise you are hearing could very well not be due to any imperfections. It is my experience that these tubes often quiet down after 50 or more hours. So I would suggest that you don't give up on using them in your MK6 quite yet. Give them some time.