Actually, he was fighting an uphill battle against Loz, Kadaj, and Yazoo in the City of the Ancients. If Vincent hadn't intervened, I think Cloud would've been done for. Of course, he did have Goestigma at the time, so I suppose that fight isn't a very good example of his capabilities as a fighter. However, I'm not denying Cloud's strength. He most certainly did accomplish a multitude of impressive feats during his time as main character. Even so, he's never done anything to really suggest that he's that much stronger than Zack, if at all.
Crisis AVALANCHE had been fighting Bahamut for approximately two hours by the time Cloud showed up. The Summon was already worn down. Yes, Cloud was able to keep up with Bahamut on his own much better than the rest of his teammates were, but the fact remains, Bahamut was still worn down by the time he showed up. Even with that in mind, Cloud needed his friends to give him a little boost so that he could actually attack Bahamut. Had his friends not been there, Cloud would've found himself unable to attack Bahamut at all. What he did was certainly impressive, but he most certainly did not do it on his own.
Zack, however, did beat a form of Bahamut on his own...*cough*
Ahem...Zack beat Genesis in his prime, beat Angeal, became a hero in the Wutai War, singlehandedly defeated a form of Bahamut along with several other powerful Summon Spirits (as in with no help from any teammates), the list goes on. However, his most impressive feat to date would be when he, as you put it, "killed Shinra soldiers." You see, you fail to acknowledge that Zack was up against about a hundred ShinRa soldiers (armed with machine guns and some with melee weapons) and three SOLDIERs (their helmets were visible after the battle) who had air support. That means he was going up against over a hundred trained combatants, all the while dealing with the helicopters that were constantly dropping bombs on him from above. In all fairness to Zack, Cloud has never done anything like that.
Well i doubt Bahamut was worn out at all.
And if you're basing yourself on a game...then Cloud alone or with help defeated a lot of monsters as well, including Jenova.
And yes you're right Cloud might have lost to all three of them (Yazoo, Kadaj and Loz) if Vincent had not appeared, yet he manages to fight them alone, and they are certainly not weaklings as Yazoo or Loz (don't remember which one) defeated Tifa and both of them defeated Reno and Rude.