• Deals TONS of burst damage. In teamfights, your Q, W and E will melt almost anyone very quickly and your ultimate will instakill them from 800 health.
• You look very, very scary due to the aforementioned fact.

AP Cho'Gath Cons:

• Expensive build. As said before, you are paying roughly 5500 more gold for your build. This means that you'll need to wait longer to get fed and not be as large as an appearance in the game until really late.
• Relies more on spells for damage. Unlike Wit's End Cho'Gath, you rely more on your spells for damage. Once all your spells are on CD, you're left to auto attack the guy you were targeting to death.
• Also relies more heavily on spells for killing in a team fight. In a teamfight as AP Cho'Gath, you are focusing the biggest threat on the enemy team. To kill said threat, you will usually need to use all of your skills, meaning that you become a big auto attacker until your skills go back up and as you have no 800 damage ult, you are not as big as a threat compared to that Tryndamere who just got a kill on their Fiora.