Kat's ulti is one of the worst AoE nuke in the game with horrible radius. It's similar to Nunu's ulti cept nunu's ulti takes time. But they're both easily interrupted. Kat's ulti reaches its peak around midgame. Once late game you'll notice there is barely much difference in terms of damage from her ulti but you'll also notice that your enemies starts to get damaged slowly from it. This is because the damage climbs very very slowly late game as you've already reached it's peak mid game. Also enemy starts building more MR and the longer the game goes, the worse it is for Kat. This is when AP does better, in terms of cost. The faster you can get the item, the faster you can deal massive damage, the longer domination period for you. But of course this doesn't mean ap kat is superior compared to ad. As said before, it's very situational. Depending on enemy composition. Certain game requires Kat to play more of the "poking" game, ad kat is better at this while some games you just need to shunpo in at the right moment and deal as much damage as possible as soon as possible, this is where ap kat comes.