For a "yardstick," try any current book on the history of photography.
What both Ansel and Edward Weston did was break away from the pictorialists and make "straight" photographs that were tack sharp and specific. Both men spent most of their time shooting rocks and vegetables. Both also shot people, but the people were posed. Both, for the most part, used view cameras on stands. Neither of them did anything really new. They just did things better.
Henri, on the other hand, grabbed the smallest camera around and began shooting people unposed. He did do a series of portraits, of which, in my estimation at least, his Ezra Pound was top of the heap, though his incredible snapshot of the Curies certainly ranks near the top, but street photography was his main thing. It's true that Andre Kertesz also did street photography with a small camera, but Andre didn't cover the world the way Henri did. It's interesting to read how many great photographers of the twentieth century single out Henri as a significant influence, among them Evans, Frank, Winogrand, Friedlander, and Leibovitz, to name just a few.
Now, notice that I said Henri was the "most influential" photographer of the twentieth century, not that he was the "best" photographer of the twentieth century. If we want to talk about "best," I'd have to make a pretty strong case that Gene Smith holds that title. But influential? That's Henri. The thing he taught other photographers was how to go with the flow and not try to put thoughts into photographs, to react rather than plan. It's something most of our contemporaries behind their cameras never learn.