all this hands most of time play in 3-bet/4-bet pots and in big pots ur opponent have a lot premium hands
With AK we block AA and KK. have 50% with QQ and have nice chance (1of3) catch top pair on the flop with good kicker and with AKs we have nice equity for backdoor flush or FD.
With jacks not all good in 3-bet/4-bet pots bcs we dont block any pockets QQ KK AA and if flop low im not sure in this hand too
So for me better AK bcs im more sure play with it, can collect more combination and can easy click pass on reraise if flop dont mine. But with jacks very often i have a hard situations and i dont care that mathematics say AK vs JJ its coin flip. I like play postflop not bingo all-in thats why i say AK
P.S. But in push fold stack 12bb and low JJ i think better bcs its ready hand