(Aside: I'm sure that tptacek could give a significantly better answer here than I can, but I'll give it a shot. (And then whenever he answers trust him more than me.))
Assume you have a perfect cryptographic hash function H(X). No matter how many of N bits of X you change (0 < N <= len(X)), on average 50% of the bits of H(X) will change. So, let's consider the case of just H(salt || H(salt || password)) versus H(salt || H(password)).
Let A = H(salt||password), and let B = H(password). A and B are now, for all practical purposes, two different random integers. Each of which has the same entropy. This is because adding the salt should make no impact on the quality of these random numbers. It should now be fairly easy to see that there is no difference between H(salt||A) and H(salt||B), other than the fact that they produce different outputs.
This is all based on the assumption that the hash function is a perfect one -- however this assumption is reasonable for strong hash functions.
Assume you have a perfect cryptographic hash function H(X). No matter how many of N bits of X you change (0 < N <= len(X)), on average 50% of the bits of H(X) will change. So, let's consider the case of just H(salt || H(salt || password)) versus H(salt || H(password)).
Let A = H(salt||password), and let B = H(password). A and B are now, for all practical purposes, two different random integers. Each of which has the same entropy. This is because adding the salt should make no impact on the quality of these random numbers. It should now be fairly easy to see that there is no difference between H(salt||A) and H(salt||B), other than the fact that they produce different outputs.
This is all based on the assumption that the hash function is a perfect one -- however this assumption is reasonable for strong hash functions.