Im getting enough ip for them, and just want your feedback on which is the better champ to buy. Ive read guides and what not on them, and they are fine. One of my main concerns is if they fall off late game, and if so which one?

Im fine with playing the role of a solotop or mid, so that isnt a factor. Thanks.

Akali is usually banned in Draft/Rated, because she is stupid good, Anivia is fine but more than once has her wall killed my teammates and myself. Though if you can master Anivia, shes pretty powerful.

If you want an assassin with CRAZY burst, get Akali.

If you want a mage with decent burst but a lot of utility, get Anivia.

Anivia was my first champion I purchased so I'm a bit biased. She has a rather steep learning curve and its inevitable that you will mess up with her wall, but in time, she can wreck really hard.

You could get both. Anivia is a great source of crowd controll in 5v5's with her high amounts of AoE slows and her stun and her ability to Nuke people, and Akali is a great distraction with her cloak and source of AoE crowd controll slows and in Dominion.

Akali is for noobs, go with Anivia, she at least takes some skill to play and she is more fun to play

Akali is usually banned, although both champions are good. Akali is the only one with a hard counter, anivia just takes skill to beat, but also skill to play. Get good with predicting opponent's movements in lane and stun them when they move in to last hit, follow it up with a frostbite and you can zone them, if not kill them. They will be too desperate to get zoned and will move in, only to get stunned and die.

Anivia is a lot more difficult to play effectively, but has the advantage of not needing a specially set up rune page like Akali.

If you're not worried about getting banned in Draft/Rated, Akali. Anivia can wreck, harass and also has a lot of utility, but you need a lot of skill and planning to make it work. Also if you kill a teammate by blocking them off with your ice wall, you will be yelled at and accused of trolling. It just invariably happens. At the same time, its still fun to play either one.