These two constructions are not equivalent, but the line between them has been blurred over the past two or three generations.
As much as, strictly, should be used only in comparisons:
Jane admires John as much as I admire Joan. ⇨
As much as I admire Joan, (so much) Jane admires John.
Much as has two distinct uses.
In one, it alternates with much like, depending on what follows,
and much acts as a modifier to the following conjunctive:
Much like me, Jane admires John. = Jane is (much) like me in admiring John.
Much as I admire Joan, Jane admires John. = Jane admires John in (much) the same way as I admire Joan.
The other use is the one which you employ. Here as has the same sense as though (and alternates with it) and much, which modifies the verb, is moved to the front of the clause for emphasis.
Though I admire him much, I cannot excuse him. ⇨
Much though I admire him, I cannot excuse him. ⇨
Much as I admire him, I cannot excuse him.
Other terms than much can be treated the same way:
Little as I admire him, I cannot condemn him.
Deeply as I admire him, I cannot excuse him.
Honourable though I hold him to be, I cannot excuse him.
These three uses are rarely confused when the clause falls in its "natural" place after the main clause. Moving the clause to the beginning of the sentence, to secure emphasis, is a rhetorical and primarily literary device; and the much as use has never, I think, fallen entirely comfortably on the ear. Consequently, there is a strong tendency to translate much as to the more familiar as much as. And it may be the case that this use, though literally meaningless, is now so widespread that it has become the ordinary idiom—witness David Schwartz' answer.
My advice would be to avoid the use. It's literary, and sounds (and reads) affected, in either form; and each form is bound to annoy somebody, either those who adhere to my opinion or those who adhere to David Schwartz'. Instead, use an ordinary untransposed construction with "although" or "even though":
Even though I admire him greatly, I cannot excuse ...