Honestly its fairly dependent on the opposing team's composition as to which champion ends up being the stronger choice. Both champions have significant weaknesses that opponents can use against them.
Akali's shroud is the classic case of "Just pink it!" for a jungle gank to shut her down pre-6th during her fairly weak lane phase.
Katarina's ultimate gets canceled by fears, knock-ups, silence, stuns, taunts, and any displacement. Get an opposing team with at least three sources of CC with those and competent players and Kat's ult isn't going to be anywhere near as deadly as it could be.
Akali has insane amounts of sustain from her passive once her gunblade is built and can gapclose multiple times to blow up an escaping priority target.
Katarina fares better at diving in and out via Shunpo to hit targets of opportunity for assists to get her resets.
Akali has an energy system to deal with, so she cannot spam the moment skills come off cooldown the same way Kat can.
However it is considerably harder to shut down a snowballing Akali than it is Katarina. Akali can drop the shroud and dis-engage with a move speed bonus to get the heck out while having at least a second to pick how she wants to juke before they drop a pink or upgraded sweeper and her high sustain gives her an edge at being able to recover health extremely fast on top of having better health scaling than Kat. A caught Kat either manages the Shunpo to safety or goes splat if the enemy team lands a couple CC.
Akali also forces the enemy team to spend additional resources to be able to deal with her at the team fight phase. While not a direct source of power it can make a difference for the rest of your team.
So in conclusion? Against a team with low amounts of CC Kat is better. Against teams with a fair amount of CC Akali is considerably better. The other consideration is AoE spam from the other team... Kat can Shunpo out of the area entirely while Akali has to hope the shroud has them miss most of it. Beyond that its more about your lane opponent and roaming. (And Akali is a safer first pick than Katarina is, not least because one to two kills can bring you back into the game far faster than Kat and your ult can't be canceled at the drop of a hat. Also that sustain!)