The sentence 'He wants to earn as much money as you do' sounds more formal as the 'do' indicates an action which is also performed by the other person ('earn money'). Now, when you remove the 'do' from the sentence, it just makes your statement sound less formal.

Both sentences are correct but "as you do" is more direct. I would say "as you" is okay too, just a little less formal.

1st for writing ,2nd for regular speaking .