Certain items are useful, on any champ or situation. Some items work really great in tantum with another item, generally being less effective without that said additional item. Some items truly shine on one champ, and are a waste of gold on the other. RoA and Frozen Heart are both great item choices for Cho Gath if he wants mana. The RoA gives him more health and AP as well, making him larger (to be honest one of the reasons we all play cho is to see how big we can get ) and the AP lets him hit harder. The Frozen heart doesn't give him AP or HP, but the armor and passive give him as much, if not more sustainability in combat. The Frozen Heart's true value to Cho'gath is that lovely 20% cdr. I run 5% flat cdr blues and +5 scaling cdr blues, so I have +5 cdr lvl1 and +10 cdr lvl18, from Runes along. With a Frozen Heart, my Cho'gath has 30% CDR with a single item buy.
If you really want that extra AP and feel like you're ahead, go for it. You'll snowball harder. If you aren't sure or if you're behind, the Frozen Heart. Ever tried getting both in the same game?
If you get a Rylai's Scepter, you don't HAVE to get Lindry's. But if you get Lindry's, I strongly suggest you DO have not only the Rylai's (obviously) but the Nashor's Tooth as well. Rylai procs off Cho's vorpal spikes, more auto attacks (fast atk spd) mean more frequent Rylai procs, since Cho I believe is the only champion in the game that can proc Rylai as fast as he can. Since his auto's don't have a cd, he can technically only be hindered by his atk spd as to how often he procs the slow. Nashor's Tooth is even more atk spd, 20% cdr (with Frozen Heart and no cdr runes this is 40%) an additional on hit effect, and improves the other 2 items. Nashor's + Rylai + Lindry is a combo you could try out. In this situation you're not really tanky, you wanna annihilate and burst people away. Wit's End, Devourer (for jungle cho) and Lich Bane are nice items to sack into this build. On AP build paths lately late game I sell my Boots (usually sorcerer's) to get an additional AP item.
Lots of words and things and ideas with concepts and numbers and stuff. Try it out! Hope you find any of it useful. I get some flak from team mates about my build but it usually stops around 23 mins into the game =) Cho can be tank, ap, or on hit effect hidden op.