When he did Cantus on Fraggle Rock or Convincing John his essence played well into each character. We was very well paced. Being a puppeteer everyday, you always have to put yourself in that character's position. What they're thinking, their thought process, how they live, what they may do off stage or off camera. How they move...etc.
Jim always had this sense of "in the moment". On screen if he was Dr. Teeth you could see the real passion of Dr. Teeth playing his keyboard and knowing he rocks it. Ernie was I'm sure one of his favorites because he could torment his ol' buddy Bert (Frank). It was his time to just be goofy. Kermit though was his cynical foil to Fozzie. Frank was capable to turn around and the same back to Jim with Kermit and Fozzie's relationship. Ernie was just so much fun for him and you could see that. Same with Kermit. He really gave Kermit a soul and a mind of his own. Even though he had control over it, you could tell he could just let go.
And that's what any performer/puppeteer does. When you're in that moment you just throw caution to the wind, find your character's inner thinkings and just let go. If you hang on to the safety rail too much it's not interesting for others to watch. Don't go over board, but get to the edge and ponder if the jump is worth it or not. And you can totally tell that's what Jim did with each and other character he performed.