Both are correct. "No one else" means no one, but with some person or group excluded. If that person or group is explicitly stated, it's redundant, but not wrong. Likewise, making a comparison implicitly excludes whatever you're comparing the rest to.
So when is it necessary? Usually when the exception has already been specified and needn't be repeated.
John is my best friend. No one else likes me more.
John is my best friend. No one likes me more than he does.
In the second example, we repeat the comparison, so "else" becomes redundant. In the first example, "else" is the only word that indicates what comparison is being made, so it's necessary.