I'm very much a breed outsider looking in but I know a lot of BCs and I consider there to be plenty enough overlap between show, sports-bred and working lines too. Especially compared to many of the gun dog breeds mentioned.
I mean, the show line dogs are hairier, have squarer heads and muzzles and are more likely to be red than others, the sports bred dogs are more jittery and more likely to be merle than others, and the working dogs have the most consistent stock instinct (including breed specific stuff like eye and clap) and the most easily trained off switch. (According to what I've seen so far.) But there's a lot of perceptible crossover from my perspective - the most dramatic difference for me is definitely the difference in appearance between straight show bred dogs and many working bred dogs which seem to lean light-coated, light-boned, slinky and pointy. The biggest/most consistent behavioral difference between lines or types that I've noticed is just absence/presence of stock sense, which is fairly narrow.
If we're talking herding dogs (excluding continentals/tenders) I think I've seen the largest gulf between working and conformation Aussies.
With Catahoulas, I get the sense that some people who strictly work dogs are definitely lamenting a great gulf between lines that doesn't actually exist yet, or are at least badly exaggerating the one that's there, as lots of Catahoulas that place well/qualify in the conformation ring also hunt, herd and place/qualify in those competitions too. Regarding that, I guess that when you're so steeped in the culture of a breed it might be easy to make a mountain out of a molehill when it comes to intrabreed variation and politics.
Anyway, I pretty much think that Labs and some of the spaniels take the cake on this one by a pretty wide margin, with GSDs following.