I think Hidan and Kakuzu would win. They actually worked well as a team when they needed to while Deidara and Sasori had a tendency to take on opponents by themselves. I think that Kakuzu would be the biggest factor in this battle since he can exploit both opponents' weaknesses. Kakuzu can use lightning attacks at long ranges and independent from the rest of his body, which would cancel out Deidara's detonating clay. Kakuzu can also use very impressive fire and wind attack combinations which should work well against Sasori's wooden puppets. He also has his nearly impenetrable hardened body defense which ought to protect him.
The only real issue I see is that Hidan's specialty is useless against Sasori. This really shouldn't be too big of a disadvantage, though, because Sasori's attacks shouldn't work against Hidan either.