The new mayor is certainly more progressive than her predecessor, but she is not nearly as efficient.

but she is not nearly as efficient
i really dont like ...as efficient ... what to say ...as efficient as...


but she, however, is not nearly as efficient
But and however here have the same meaning

but she is nearly not as efficient
nearly and not should change their places

is nearly not as efficient
awkward

even though she is not nearly as efficient
even though - not good as but she is not

despite being not as efficient
incorrect

I vote for A instead of D because it is more concise.

but = Even though in this context.