Same here, my exposure to TMS as a kid was very limited at best, but I always had the movies on tapes to revisit whenever I wanted, so when I think of Beauregard, the first thing that usually comes to my mind is him as the taxi driver in GMC, which I always enjoyed: especially how Kermit quickly picked up on Beau would always go in the exact opposite direction of where they told him to go.
But another thing to remember about Beau is that one of the main reasons they created the character was, in a sense, to make a Wendell Porcupine-esque character for Dave to perform on a regular basis since Wendell was something of a break-out character from Emmet Otter.
As for what makes Bobo work better, I think a lot of that has to do with Bill having so much clout with the Muppets; notice how most of the more recent characters to the lineup are mostly his: Pepe, Bobo, Johnny Fiama, Big Mean Carl, they're all Bill Barretta characters. It's similar to how Elmo became so big on SST, because of what Kevin was able to do with him.