I love Chaplin and Keaton. They were very different types of artists and comedians, and between the two of them I think they covered the human experience. To me you cant make them compete with each other, because they compliment so perfectly.
Calling Chaplin overrated seems a little crazy to me, because if anything despite being iconic, i think hes a little underrated. I don't think many people realize that he was like 100% in creative control of everything he did - apparently he did everything down to the score, and in some cases, the makeup for the cast.
Have you ever seen Limelight?
Its the only time they every worked together, because they were rivals in the day, and its kind of sad because they both play sort of pathetic aging clowns. And since it was a Chaplin film, he cut some of Keaton's best stuff - still maybe feeling that competitiveness even in their old age. I liked the whole movie, it was sad though, but their scene together is definitely worth the watch.
Thats the only photo from that era that I think they both are in...
I also really like Fatty Arbuckle. But the silent comedian I never understood the appeal to was Harold Lloyd. I liked Speedy, but I don't know.. he just doesnt have the same charm or artistry in my opinion.