i disagree with the above, akali rapes katarina in lane.
Katarina is an awesome and fun champion to play, but simply and plainly useless at higher level... unless you play with a good morgana who shields you during ur ulti, or if you ahve galio or amumu in your team.
Akali, on the other hand, is also very fun but much more viable, especially if ennemy team consists of squishy, and she has awesome skinz as well, with nurse akali on sale at the moment
So if I were you, i'd buy akali. She is free to play like once a year, whereas katarina is on rotation every month.