Maybe a natural way of saying what you mean to say, especially in conversation, would be: "I trust you more than anyone" or "there's nobody I trust more than you." I've also heard "I trust you like no one else" or "I trust you like nobody else." I suppose you could say many things to convey the same thing, but these few sentences would sound quite natural to me!

"I trust you like I trust no one" This one means I don't trust you. You should add the "else", as Nanren noted, to mean you trust that person more than anyone you have ever trusted. Technically, the trust doesn't have to be greater than other people, but I think a native speaker would understand the implication. "I trust you as much as I trust no one" Even if you add the "else" to this sentence, I don't think it would make sense.

Sorry, but no meaning is clear to me from these sentences. . I trust you like I trust no one else? I trust you more than anyone else? I trust no one else as much as I trust you? . Unless you are talking to a non-human, I guess.

Both are good, however for me the 2nd sentence seems more ambiguous.