Katarina...

How is Katarina going to survive the mage rework when basically any item that isn't Gunblade or that belt will give her any real stats? Sure Gunblade is okay, but the only thing going for her with Gunblade is the active at this point; Omni-vamp isn't viable considering her only single target ability is Shunpo. Her only savior item, Hourglass, is being nerfed and may push her out of the meta. She doesn't get the fullest benefits of Abyssal either besides to save her from LB, or some other mage that counters her. She also doesn't exist in professional play (anymore) because of her ultimate weakness (coordination).

Now, what if we built AD?

The problem with AD Kat is that it's too weak. Sure she has some AD scalings, but these aren't very effective considering all of her abilities do magic damage, and the fact that they're only bonus AD scalings. She could build AD only if she could benefit greatly from it. She also doesn't have dual penetration, unlike Kayle, and she doesn't have the burst Jax does when you pair him with Attack Speed. Before the AD rework, it was more viable to build AD Kat, only because the items gave more AD than they did now. She's also very clunky to try to play as AD despite the fact you can AA and W at the same time. Your DPS suffers from using Death Lotus because point for point, Bonus AD isn't as powerful as AP despite it being 3.75 vs 2.5. You can build glass cannon to try to make up for this, but... you'll probably get burst much more quickly than if you went AP. You either have to build some attack speed, causing your W and R to suffer in damage, or go full AD and watch yourself suffer when you can't out damage your target after you blew everything on them with only 2 scaling abilities.

Another thing I should note about Katarina is that she's a one trick pony. Sure she can reset off the low health squishies, but what about late game? AP Kat falls of because MR reductions is so easily available by anyone, and AD Kat doesn't have any real penetration unless she makes sacrifices to her DPS or Burst to make it happen.

tl;dr AP Kat is kinda crappy, and will (probably) be more crap because MR and Mage update, AD Kat is a bunch of crap because the tradeoff isn't worthwhile versus Overloaded ADCs and better AD Assassins that outburst her.