The steel makes no difference, it's the razor that's important. I've had and still have absolutely fantastic razors in stainless and non-stainless steels.
I am pretty sure every person who has been around for a while and tried some of the top razors will tell you the exact same thing. Also I have not yet found a current production razor to shave as good as my best vintage ones. But I've only tried about 150 razors so far with less than 10% of them being current production ones.
Of course, it all depends on what's important to you. A bit over $100 will get you the tortoise special which I personally consider an upgrade to what you have. To access stainless steel razors you're looking at at least $150 and at this price point you can actually get great vintage one. But you have to know what to get and be willing to overlook insignificant defects, like warped scales or few of speckles of tarnish.
Anyways, good luck in your search.