You have to put 'one' after 'same' because same is an adjective and has to modify a noun. In this case, one is functioning as a relative pronoun relating back to the only noun mentioned in the previous sentence (i.e.: 'home').
You could change the 2nd sentence if you like to: "It wasn't the same as before, but at least it was safer." In this version, you would be referring to (the time when you lived in the previous home) and the function of same would be as an adverb allowing for the omission of 'one'. Or you could do as Jack O'Flaherty advised and write 'home' instead of 'one'. All are acceptable solutions.