Very different steels.If the ATS-34 is cryo treated,it will come quite close to O-1 in edge sharpness.The O-1 will rust and may chip a little easier than the stainless ATS.If you are making a kitchen knife,go ATS,if it is a bowie,use O-1.You can HT the O-1 yourself much easier.
Remember - sharpness is only one part of a steel choice,and in my opinion it is not the most important.A tin can can be sharpened to shave hair,and glass is 100 times sharper than steel.
Stacy