I don't think you're missing anything per se. The Chunky Cheese (and obviously the Big Cheese it is based on) are just fuzz pedals and there are countless different variations and options because tastes differ so widely.
For me the attraction was that it checked almost all the boxes I was looking for with a fuzz:
- It worked well with active basses
- It was more aggressive sounding than "farty" or too nasally.
- It didn't have a built in mid scoop that made me disappear in a mix.
- And it could do gated sounds that were still stout and not "dying battery" like tones.
The only thing it didn't have was good low end retention or a built in clean blend.
Personally I totally dig the sound of a blended Chunky Cheese - just raw and biting. In fact tonewise I liked it more than the Brown Dog that I kept. But the need for the blend and the Chunk's greater versatility led me to sell it.
That said, if there was a Chunky Cheese modded with a good clean blend I'd absolutely give it a whirl again.
But that's me. If you don't dig it enough to deal with the hassle of a blend then don't worry about it and find a fuzz that works better for you.
Hope that helps.