Killing Jack as of right now doesent really change the story beyond how 2 characters treat you, a few dialogue lines, your corruption level, and your power stat
Killing or sparing jack doesent really boil down to right or wrong but what route your trying to go, and how much your willing to potentially deal with down the road if you spare him, hes the strongest known mind controller besides maybe melody(given the fact that Jack is the spawn of an apostle i would venture to say he is definitely stronger or will be in the future), H.E.R.O. could become a real thorn in your side later on if they have jack at their disposal, so it really just depends on what route your going through and whether or not you want to break away from hero in the future If WeirdWorld chooses to diverge the story like that, personally i have two saves one where i killed him and one where i didn't because i feel like it will play a big part in future updates