I'm wondering which one of these I should choose for a good AP carry

Anivia has good harrass and is pretty forgiving to learn with her egg. Vlad has a slow early game and is a hard to kill aoe boss late game. It really depends on what you're going for. If you suck at skill shots, and don't do well with positioning skills like alistars headbutt or singes toss, I'd say go with Vlad. Anivia's wall placement can mess up whole teamfights if you drop in the wrong spot/time, but Vlad is pretty straightforward.

Vlad is way easier to play. Not mean he doesn't take skill, it's just that Anivia is F**** hard to play with. One mistake means death, unless they are low level, than they won't be able to kill your egg.

You also forgot Karthus.

Anivia is definitely the highest skill of the three (imo) and (also imo) lacks a fair reward for the level of skill. She is definitely a force to be reckoned with, but requires a bit of team help/coordination for maximum effectiveness.

Vlad can hold his own and is fairly easy to get good with. It's not uncommon for Vlad to score quad and penta kills in teamfights due to his amazing AoE damage output + sniping squishies for 700 with transfusion.

Karthus is in my opinion the pub stomper. Once you get good with him you can easily out lane any non-Kassadin mid, make up for your teams mistakes with your ult, and do enough damage mid through late game to single handedly ensure teamfight wins.

TLDR;
Anivia is for playing with your good friends.
Karthus is a pub stomp
Vlad is inbetween the other two.

Karthus plug: (all are solo queue :P)

Lol...you lost 2 games later(Yes I'm bored enough to look it up)

Both anivia and vlad are really good.

Anivia is a really good comboer, but very easily squished. Her egg can be really helpful, but over very hard to play especially the placement of her wall. If Anivia's wall is placed too early ppl can get away, and that doesnt really help. Need to be careful especially where you place yourself because if you're in the wrong spot at the wrong time you can go down REAL fast.

Vlad is a little more forigiving I'd say. He has one of the best escaping skills b/c he can't be targeted while using it. Vlad can be a really good carry. He overall has really good skills that do really good damage. Vlad can be aggressive, and doesn't need to worry too much about dying really fast in team fights. Plus Vlad can tower dive to get kills and escape with his Sanguine pool D: I was playing koggy wen one vlad did that to me...=not a very happy kog'maw

It's a hard pick, but I'd choose Vlad :P Depends on your game style.

Not sure if troll question.
Anivias wall is one of the best isolation spells in the game.
Not to mention she actually has (small AoE) CC. And she deals easily as much dmg as Vlad.

Anivia 100%.

i would go with vlad he is amazing he can escape pretty well and is not very squishy deals lots of damage and is really fun to play

I personally play Vlad as my main, Im not the best but I would recommended him if your good with positioning yourself to do the most AoE possible, aren't uncomfortable to get close to the enemy (not to close) and just play him as a caster.