As I look on your profile - and I believe it's not a smurf, according to your score every game - I highly recommend neither of these two champions. They might look cool to you but if your average score is 4.9 / 10.4 / 6.9 and you do this terrible with Annie, your game knowledge is so bad that it doesn't let you to focus on controlling your champion, which is very important with both Katarina and Zed. You can, of course, try to play them, but you are going to not even know where you are and it is going to frustrate you beyond your imagination, leaving you with no enjoyment of the game. I recommend watching at least few videos on Youtube (try Tips for Bronze and Gold from PentaMagic channel, it helped me ALOT when I was a beginner) playing champions you don't need to focus on that much, then move to harder ones.
And then I would recommend Zed over Katarina, while she is potentially better at damage dealing (she can slay the whole team while Zed cannot take more than 2 people per teamfight out if not insanely overfed), she does also require way more thinking about her engaging and comboing in the middle of a teamfight.