Ok I know this is a controversial discussion that many people would say is one-sided; Cloud is better. I on the other-hand don't see it. I mean sure Cloud is awesome, but he's no way near a better hero than Zack.

Let review shall be:
Crisis Core- Zack kicked ass in this game. He defeated some of the most iconic summons in FF history as well as 2 of the strongest 1st class SOLDIER operatives, Angeal and Genesis. He had to fight and kill his closest friend. He was then betrayed and hunted down by Shinra just to cover up that Sephiroth went crazy. To save the life of his friend, Cloud, he fought against an army of SOLDIERs, my guess is all 2nd class. And then he died, not even being able to prove to the world that he was a hero, and the only person who new he was a hero was Cloud.

FF7- Cloud forgot his past and took over Zack, whom he admired greatly. He then goes on his own journey to fight Shinra. When Sephiroth reveals the truth to him he becomes even more depressed (well to me that was the case). He eventually defeats Sephiroth and is renowned as the new hero.

FFAC- I don't want to go too in detail so I suggest that you watch the movie, "Final Fantasy Advent Children." To cut it short, Sephiroth returns fights Cloud again and Cloud wins in the end.

I don't know, to me all Cloud did was fight and never gave it a second though. He never truly lost anything. Zack, now he as a guy that lost a lot. Lets see Zack lost: the respect of his fellow SOLDIERs, his best friend, his girlfriend his own life. He died in a wasteland where no-one could shed a tear for him, except for Cloud. To me he really is a HERO of the Final Fantasy series.

Feel free to disagree if you want or add something important if I missed anything.