You could say it either way, but "was as much of a success" is better.
"As much" needs to modify a verb, adjective, or adverb. (I'm not 100% certain on this, but I can't think of any case where it would directly modify a noun.) "Success" is a noun. This means "as much" is describing "was", not "success", so it sounds a little strange when it follows "success". It should follow "was", not "success", in the sentence.
Instead, you could also say "Successful". "It was successful as much as we expected." In this case "as much" modifies "successful", and comes right after it in the sentence.