AP Cho'gath is better.
Why?
Cho'gath lacks the traditionally short cooldowns and reliable crowd control to actually function as a tank. He cannot engage like Sejuani, Malphite, Amumu, Zac, Leona, Braum, Ornn or even Rammus, and even with his E and his Stoneplate + Feast combo he usually does less damage than most of those champions. If he does not get fed enough to one shot with Feast, his target will survive and Cho'gath will be useless for the next minute. He lacks options to peel for his allies, which is extremely apparent when compared to champions like Galio, Maokai, Braum, and Poppy. To make matters worse, he is incredibly easy to kite, and, sadly, even with high resistances, his infinitely stacking health does not matter thanks to the plethora of easily itemizible % HP damage in the game. There's also the problem of where to lane tank Cho'gath. If you take him top, you likely have to run Teleport, but Cho'gath has relatively little ability to make use of the Summoner Spell thanks to his poor options in ganking with it and his fairly weak splitpushing. If you run Tank Cho'gath in the jungle, your team has little to no early pressure, and Cho'gath is denied access to a better gold stream. If you run him mid you have denied your team of a more effective source of damage, utility, and waveclear. He also does not roam very well to assist other lanes.
While AP Cho'gath still has some of the same weaknesses, he has less overall and has greater strengths. For example, the monster mage's large health bar becomes an asset to protect him from assassins and burst damage rather than a liability for your team as a result of an enemy's Blade of the Ruined King. As AP Cho'gath itemizes more mana and fulfills a different role on a team than a Tank Cho'gath, his Q and W can be used more frequently and are less punishing to miss. AP Cho'gath has an easier time fitting into a team composition, as you are able to play to his strengths, rather than trying to make him something he is not.