I know some of the rarest colors are often inbred and not as healthy as normal budgies, and I would guess also not as intelligent. But I think most of the more common colors have been around long enough that they no longer need to inbreed to maintain the color so I don't really know of a reason for difference in intelligence between common colors.
All I have is a little green budgie and he's pretty smart.

Karen
Chico (conure) and Pippin (budgie)
WI

I think you are absolutely right here....green birds are the most intelligent ones as i have seen.
I have a very young green clearwing, i think he's gonna be very very smart too......Do you think
clearwings are inbread???I also have a blue dilute clearwing, which is not very bright, but then
she is just recuperating from a very long illness.... I do not expect her to play with me but still
I think normal green male birds are the smartest.....

I don't really know much about budgie genetics but I think that's a common color, so inbreeding wouldn't be necessary to produce it. My Pippin is actually a greywing green, so he's in between the normal green and clearwing. And he's pretty smart; he doesn't have an exceptional vocabulary (only about 100 words) but he knows exactly how to manipulate people to get whatever he wants.

Karen
Chico (conure) and Pippin (budgie)
WI