2) Of both of the boys, Leo is better. or. Of both of the boys, Leo is the better __(e.g jumper, runner)__

Neither. Of the two boys, Leo is the better (one).

Of both the boys,Leo is the better (boy). The word "boy" is understood, and that's the meaning. Or you might mean this: Of both the boys, Leo is the better reader, or better student, or better behaved (boy). Of both the boys, Leo is better. You would say this if someone asked, "which boy is better?" Both of these would be okay. You would then explain your answer, why, in your opinion, he is better. When you compare two people or items, you use "better". If you compare more than two, you can use "best".

"Leo is better" is correct. "Better" doesn't have any "the". In the other case, after "the" you could say "best".