It is the difference between "as much/many...as" (autant (de)...que) and "as...(adjective/adverb)...as" (aussi...que).
Elle n'a pas autant de chats que sa sœur.
<em>She doesn't have as many cats as her sister.</em>
Il est aussi intelligent que vous.
<em>He is as intelligent as you.</em>
Ce comédien ne joue pas aussi bien que mon petit ami.
<em>This actor does not act as well as my boyfriend.</em>