Chagaev would murder Pulev. Pulev at his best might have a better jab, but literally every other technical matter from slipping, to footwork, to punching, is Chagaev. Wide UD.
I respect Pulev, but McGrain is right. The only thing that would give me any pause at all is that one of Pulev's worst selling points that he's demonstrated is not really a problem with Chagaev. In that I mean Pulev cannot be dissuaded from fighting tall against people taller and better than he is. I don't blame him. It's difficult to train that out of a jab merchant who is 6'4. Once you're 6'3, 6'4, the likelihood is you're not going to get it through your thick skull that you are not relatively tall in a way that affects how you box. At that point, you're tall. It's in your mind. You're taller than almost everyone on the planet. Now, when you're up against someone 2 inches taller...you're still tall...it's just... Well, anyway, Chagaev is a midget for a heavyweight of the last 20 years. Maybe Pulev would have some significant success but he actually even fights like he's not only tall but a giant. He does the snake charmer like he has a foot disparity to play around with, when that's never the case. And the jab is good enough that against F, D and C-levelers...He will and does get away with it. Chagaev didn't even let Valuev do that. I don't think he's going to let Pulev get away with it either.
Another vote for Chagaev. Pulev isn't going to be able to keep chaggy at range and that means he's going to have to go to war with him. I don't totally discount Pulev, but I would make Chagaev a solid favourite in this, I think.