Warning: Some of my thoughts are non-canon and just based on my own ideas
I think of it as Dr. Teeth is the actual leader/founder of the band. Floyd is his right hand man, who is a little more sociable. During performances, Dr. Teeth is loud and energetic, but when the band is not performing, he is often quiet and calm, while Floyd is more likely to speak out. I know that a big part of this was the Jim was usually performing Kermit in group scenes, while Jerry was usually performing Floyd, but it still lead to this effect. Floyd is obviously close with Janice and has been tasked with taming Animal at times, which often leads to him appearing like the band's leader. I still believe that Dr. Teeth is the band's true leader.