One isn't better than the other, they mean different things. And neither is a common phrase by itself. You GO into the deep, but you ARE in the deep. Some examples: "He was swimming in the deep end of the pool." "Don't go into the deep end of the pool." "I'm in deep trouble." "I'm in too deep." (The phrase "in too deep" means you are too involved in something to get back out.) "She descended into the depths of the ocean."

"the deep" as a noun is used only in literary contexts, and so its use may not always be standard. The correct preposition will be governed by the verb and the subject's relationship with "the deep". e.g. The ghost ship sank into the deep and was adrift for weeks in the deep. Your question should be "Which phrase is better ... or...."? The word order of English questions is not the same as in Italian.