JJ has a 57% to win against Ak unsuited and 54% to win against AK suited so in theory with AK you are an underdog. However, if you are playing with a maniac things quickly change.
AK is premium hand, so AK is better. More chance to win with it especially at pokerstars. Usually when you get JJ, QQ or KK there are always Ace on the flop. In deep run and with good stack when you get one of those pocket hands better to slow play, and if there are Ace on the flop and villian goes all in, my opinion just fold it down.
I don't feel very confident with JJ, it's deffinetly depends on situation but what I notice that very "unlucky" couple. It's not a rule of course. I prefer AK
I believe that any pocket pair is always better than other two cards, even Broadway cards. Any pocket pair is always a made hand and gives you a much better chance of making a monster on the flop. Ace King is just an Ace King.