Because fungi have already taken a turn or two breaking it down, in one sense it can "be comparatively stable", since it is well on its way to being rich soil. On the other hand, the fertility may be low because a lot of the nutrients that were in it may already be used up.
I would second the idea of using a mix of both the mushroom compost and the wood chips, because then you are amending with different elements of the succession. Wood chips attract the primary decomposer fungi, while the mushroom compost feeds the fungi that
feed on decaying fungi that fed on other fungi.