Curly. Yes, he had to retire after his stroke, and they did plenty of funny work without him, but there’s no way they’d still be so well known without him.
Oh, a wise guy, eh? (drags Gyrate around the room with a clawhammer in his nose).
Subtle and sublime are not words I associate with a Stooge. That’s like saying Zeppo was the best Marx Brother because he ended up with the most money.
I’ll watch Moe, Larry, and Curly – no question. But while Shemp and Larry and Curly would be worse, I’d find it to be, uh, less worse than Moe and Curly and Shemp.
Moe Lite can work, a bit; but Larry added something weird and offbeat and unique.
“I’m having Shemp, Moe, and Larry.”
“That’s still got Shemp in it!”
“Not as much as Shemp, Larry, Curly, and Shemp.”
Who edited ***Cosmopolitan ***and went “Nyuck, nyuck, nyuck”?
Helen Curly Brown. 
They were The Stooges first, tho, so singling him out doesn’t necessarily revoke his Stooge-ness. IIRC they were only really credited as Iggy and the Stooges after Ron passed away in 2009. I still think it was a mistake to do this, as bad as a “Joey and the Ramones” would have been.
I figured Curly would be in the lead, he always wins as people’s favorite Stooge, he could be considered the funniest Stooge depending on how you define it, and he was undoubtedly the best at the physical humor that was a large part of their appeal. But since the question is about the ‘best’, I’ll define ‘best’ in any way that results in Shemp as the answer. Shemp had the real pathos, he was the most human of the Stooges.
Moe’s talents are sometimes short-changed, if you get to see the documentary series made by his son there’s a scene where Moe did the alphabet song in Japanese, late in his life, as vocally nimble and entertaining as he had ever been in the age of the Stooges.
Also, there’s a special place in Hell for anyone who votes for Joe Besser. Yes Virginia, Joe was a real Stooge, but he was the worst Stooge.
I voted Curly, but Shemp was okay. He was one of the original Stooges, after all. Curly replaced him after he left the group, and then Shemp returned after Curly became ill.
I always looked up to Moe. He was sort of a role model for me.
Emil Sitka was from my hometown, Johnstown, PA. 
Here’s a publicity pic of Emil as a Stooge, with Moe Howard and “Curly” Joe DeRita. He named himself Harry, in honor of Larry Fine, whom he replaced.
You must be really short!
Off camera: Moe.
On camera: Curly.
Moe had the smarts and perseverance to make things work for a long time. But it was Curly who shined brightest.
Compare Curly to the fake-Curlies that followed. None of them did what he could do as a Stooge.
And at least Joe Besser wasn’t a schmuck. He did some good non-Stooge work. I still remember him from The Joey Bishop Show (sitcom). (IMDb says he had more appearances than Abbie Dalton. Wow.)
Don’t recall anything good about Joe DeRita as a Stooge or not.
Emil would have made a fine Stooge.