We really can't accept either of these accounts as canonical, since Alan Moore wasn't involved in either of them.
However, we also shouldn't believe anything that The Comedian says, considering the kind of man he is. While it is easy to believe that he was capable - and probably willing - to kill Kennedy, it is also very easy to believe that he would lie about killing him, if he thought it would impress the people around him. As far as I can recall, the only evidence we have to support the claim that The Comedian killed JFK is the implication he made about it at a party (see the image included in a previous answer).
If you know anything about The Comedian, you know that he can't be trusted. His word is meaningless. He's a degenerate, a murderer, an attempted rapist, and an all around horrible person.
Thus, if you prefer the version of events in the movie, you are free to accept that account. If you prefer the version of events in the Before Watchmen miniseries, you are free to accept that account. The only thing you shouldn't do is take The Comedian at his word.
Since Alan Moore has all but disowned Watchmen, especially the adaptations of it, we'll probably never know what really happened between The Comedian and JFK.