Im guessing kates decks are supposed to be equal in power to your own? I have a decent deck but I hate the fact kate brings out DJ Korr Cr or some top tier GHEIST against my sentinal -_-. I always seem to draw the weaker cards in my deck vs kate and then kate seems to have the best cards in game...sheesh...
Use a low-star deck (20* or lower). then Kate will use only 3* or 4* cards, some of which aren't fully evolved so they have bad stats and no ability. you'll be able to win easily if your own cards have decent abilities :)
Kates decks are based on your * count I think not so much the cards.
So if you use a lot of 5* cards kate can use most 5*s
Easier trick is to just 2-4 pill round one. Normally she counters with an 8-10 pill, thus giving you an easily winnable 2x pill advantage.