In my books 2 completely different beasts.
The 37C was for me a very harsh and unforgiving razor...one of the least smooth I have ever tried possibly. I did not find the shave extremely close (let's say R41 territory), but the harshness is certainly comparable.
The S1 on the other hand is one of the smoothest and most forgiving razors in my den. I still have it (SS on a Colossus handle) and it is my trusted travel companion. I have tried it on 7+ days of growth as well as a daily driver and everything in between - always with the same result: smooth and efficient.
It is very nimble (very low head profile), however probably not the super closest razor out there. But if you have only 5min for a shave at 3am in an airport hotel after a week of traveling, that's the tool you want to have on hand.
I am fortunate enough to have some nice razors in the den, so at home I don't use it too often - but that's only because of the looks. It is a very nice tool, but not a gem like some of the others I have. It looks and feels of course way better than the 37C.
In terms of shaving quality on the other hand, it can take on all the other bad boys in my den.