In American English, both structures are fine in both sentences. "As" is slightly more common. In casual speech, we'll often use object pronouns, and then you HAVE TO use "as". You should avoid this structure in writing, but in casual speech it is more common than the "correct" version: "He has the same shirt as me" (casual)=he has the same shirt as/that I do (formal)

it should be "i have the same book that he does", and "Israeli military authorities controlled Gaza in the same way as they control the West Bank"