Hi Spydutch.
ATS55 has slightly less carbon, but it has cobalt copper and silicon in it which ATS34 does not have. There is significantly less molybdenum in ATS55 also but slightly more manganese.
What this means is differences in the the corrosion resistance most likely due to the copper in the ATS55. The cobalt in the ATS55 sort of makes up for the lacking in molybdenum in some ways but the real difference I see is that there is copper, cobalt and silicon in the ATS 55 which comes together to probably create a steel that can be harder and quenched at a higher temp. The reason I say that is because the cobalt generally intensifies the other elements somehow and both it and the silicon increase the strength and hardenability of the steel. The copper seems to tell me that the ATS 55 is probably going to have better corrosion resistance also.
Of course all of this is just an educated guess. I'm not a metalurgist so maybe one of the other guys can zero in on more for you.