Resolution vs Extended Resolution
Your definition of $D$ is not clear, if it is $D = \max_f (R(f) - ER(f))$, then it is exponential.

There are DNFs whose shortest proofs in ER is exponentially shorter than their shortest proofs in R e.g. PHP (pigeon hole principle) has polynomial size ER-proofs but only exponential size R-proofs.

Unsatisfiability of $f$ is the same as $\lnot f$ being a tautology. Let $\lnot f$ be as PHP. Then $R(f)$ is exponential where as $ER(f)$ is polynomial, so the difference is exponential. Also it cannot be more than exponential. 

Addendum:

If $D =  \min_f (R(f) - ER(f))$ then it is 0. Take $\lnot f=\top$ and it has one line proof in both. (R is included in ER so it cannot be less than 0.)