@Meddler Cho'gath should be an AP juggernaut.
So Cho'gath has some changes coming up to make him a cooler tanky dude and deal more damage while being tanky, and that's great! Cho'gath's main appeal has always been in being a gigantic eldritch monster who can take a huge amount of punishment and then dish it out.
Which brings me to my point. Cho'gath is a champion who doesn't really fulfill the identity he was meant to, IMO. Building full tank makes you very hard to kill, yes, but you're easily ignorable because you don't really have a tank's kit. He has no way to put himself into the backline like a Vanguard does, and his utility is too low to make him an effective warden (also his CC is too fucking slow and telegraphed). Building him full damage worked a bit in season five, but the game has moved on, and now he just gets gunned down like the degenerate he is, being way too immobile to warrant a build that squishy, and with very unreliable abilities that don't synergize well (his Q and W are ranged abilities that don't do much to bring him close enough to use his sustained damage E or his burst damage ult). Going some damage and then full tank just means you don't really do much damage, nor can you effectively tank, and your kit is still a mess that doesn't mesh together very well and is very telegraphed.
So I've thought about what identity he should have when his inevitable rework hits, and it seems obvious that juggernaut is the answer. Cho'gath is, first of all, an incredibly immobile champion. This already distances him from every tank, who have ways to jump in and lock down/engage the enemy team, or the ability to rush to an ally's aid. Even Nunu, probably the most immobile tank, has a modest MS buff at his disposal. Immobility is also the defining characteristic of the juggernaut class.
Furthermore, it just fits the theme of Cho'gath the most. Cho'gath isn't some incredibly durable wall who wants to use his crowd control utility to set up kills for his team, he's a gigantic forever hungry monster who wants to devour all of Runeterra and destroy it, as seen by his ult. Nor is he a squishy backline mage who wants to kill enemies from afar and avoid duking it out with assassins or bruisers. He's a giant monster whose physical power swells as he consumes matter. His most iconic ability, his ult, would seem to support his role as a juggernaut, since it is simultaneously an ability that encourages him to get up close that deals a huge chunk of damage, as well as giving him a big chunk of health every time he uses it to make him harder to kill.
Furthermore, I think it would be best if he was a champion tailored toward scaling hard into the late game. His theme does support this, as he starts off small and frail, but as he gorges himself on enemies and levels his ultimate he becomes bigger and hardier. More than that however, is that right now juggernauts as a role don't have much variety in their power curve. They all, with IIRC not a single exception, fall off in the late game. Before that there are some variations, with Illaoi having a particularly powerful laning phase and falling off particularly hard later for example, but this is true of all of them. Even Nasus, the most late game oriented juggernaut, actually spikes in the mid game (when he has a good amount of stacks, becomes impossible to duel which makes this splitpush-oriented phase of the game good for him, and before enemies have pen items), before falling off to be merely "all right" at best late game. It would be refreshing to have a juggernaut in the game that is pretty non-threatening early on, but eventually scaled into a huge badass.
I don't know how his kit should look to make all of this possible. I do think his current passive should probably go and he should get some more reliable combat sustain, and that his abilities need to synergize more with the rest of his kit (maybe making his stomp knock enemies towards him would be a good idea), and maybe even make his ult less of a single target no counterplay nuke. I think that AP fighter itemization should be looked at, because as of right now it's honestly kind of awful,and part of that I think is due to AP champions not getting AD scaling on their autos to help their damage (I guess Cho's E was meant to alleviate this weakness? But that just means he loses an ability to have what AD champions get normally), as well as the lack of a penetration item that also provides defense in the same way Black Cleaver does.
Anyway, this post was more disorganized than I hoped, but thoughts on the general idea?
tl;dr Cho's theme, design, and even to some extent his kit indicate he should be an AP juggernaut, and a weak early/strong late one at that.