Cho'Gath isn't a killer.
What I mean by this is that his role on a normal team comp is not to have the most damage. His mid and ADC allies should be able to kill all the enemies.
Cho'Gath wants to be in the middle of a group of enemies, being as annoying as possible. The more distracting you are, the less your opponents attack your carries, and the more time your carries have to kill people.
Having Feast stacks makes you more unkillable. It is almost always worth killing a minion to get a Feast stack as soon as Feast is back up, unless you know that a team fight is imminent. The more damage you can take before you have to run away, the better, and Feast stacks will help you do that.
AP Cho'Gath is not the optimal way to play Cho'Gath, to be honest. It's fun, for sure (he's one of my favorite champions), but he's not going to be effective in a truly competitive game. For this reason, I think the specifics of timing Feast when running this build aren't as important.
The only difference between AP Cho'Gath and Tanky Cho'Gath in terms of Feast timing is that you might want to be a little more conservative spamming it on minions when you are trying to go for kills. You still want to build stacks, but if you think you might be able to get a kill, then save the Feast for that. Just don't save it too long. You want to be using Feast so that you can use it again ASAP.
If you know you're about to die, and you have minions available to Feast, you need to make a quick decision. You're going to lose half your stacks either way.
If you have an even number of stacks:
- Don't bother feasting a minion.
- If there's an enemy nearby, and you're a high level (enough that it'll cool down by the time you respawn anyway), just Feast the nearest enemy champion so hopefully your team can avenge you.
If you have an odd number of stacks:
- Feast the nearest enemy minion. You'll have 1 more stack after you respawn, which will help you get up faster.
Additionally, if Feast is up when you spawn, glance at your own jungle (even if you're not the jungler) to see if there's a safe Feast choice. The sooner you Feast, the sooner you can Feast again.