He likes travelling as well as you do./He likes travelling just like you.
He hates going shopping as much as you do.（as...as之间有多种副词可用）/Both he and you hates.../You hates going shopping and nor does he.
He is the same as you.没错,是最直接的翻译.但直接说两人相同意义上有点说不通,最好是说两人某种性质的相同.
也可以是He is alike with you.吧.(这句只是凭感觉写的,不知对错)
个人认为He is nothing different from you.最合适.
the same as是固定搭配,the不可少,也不可改为a.