The as ... as construction and the much to phrase should be parsed separately.
The subject is ... as different from ... The Artist as you can get
This compares the subject of The Search to that of the The Artist and states the the difference is the greatest you can get: “You cannot get a subject more different than The Artist”.
...—much to the annoyance of some of his critics and fans.
The much to NOUN idiom is a sentential modifier meaning approximately that the eventuality described in the sentence “caused much (or great) NOUN”.
Much to my dismay, I found that someone had stolen my wallet. ... The theft caused me much dismay.
John returned uninjured in November, 1918, much to the joy of his family. ... His return caused his family much joy.
So in your example, the author states that the great difference in subject between Hazanavicius’ two films greatly annoyed some critics and fans, who doubtless hoped that the second film would be more like the first one.