Any steel made to the same exact specifications will behave the same regardless of where it has been produced. As long as the composition is the same the mechanical properties will be the same as well.

Far more important is the question of heat treatment. That's as much an art as it is a science. It's the heat treatment that either brings out the best in the steel if done correctly... Or you end up with a blade that performs worse than it could because something wasn't done right.

Heat treating most stainless steels is inherently problematic because it takes a lot of expensive equipment and a good deal of experience (more than the Chinese shops producing SAK knockoffs can afford). That's the reason why a select few manufacturers can make much better blades out of the same steel than the competition.