I actually agree more force and superior Haki usually result in better AP, but it's not the case always which is what happened with Zoro and Luffy. They both tried their luck against a common defense and Zoro came out on top which proves Zoro's AP is better.
Also, If you think about it, the Scabbards were able to hurt Kaido better than pre-Udon Luffy—even though their attacks are nowhere near as powerful—because they have a higher level of COA than pre-Udon Luffy. So your attacks work more effectively on Kaido the higher your haki level is; basically, a noob with barrier COA would be able to damage Kaido easier than a city buster with level 1 COA. Now apply the same to Luffy and Zoro, Luffy's attacks should be more effective on Kaido due to penetration than Zoro's, yet Zoro hurt Kaido more implying his attacks, in general, are actually more powerful.
I did not say Zoro hurt him better only because he cut him. Zoro's Tatsumaki was the first-ever attack that made him vocally express that an attack actually hurt him:
Meaning he did some damage worthy of acknowledging although it's still insignificant.
With Asura though, Kaido was visibly distressed which is evident from him expressing his agony by saying "damn it" while looking at the wound holding it which puts a special emphasis on the damage done and implies that it's significant.
Even when Zoro was disappointed that he did not knock him down, Kaido assures him—notice how he's shivering while saying it—that he did enough damage, once again, implying the damage inflicted is significant.
Also, Kaido started huffing, even while talking, after Asura:
Zoro said nothing before blocking the attack. Luffy had plenty of time to at least attempt something b/w the time when he saw the attack coming and when Zoro blocked it, but he only started moving after Zoro blocked it and told everyone to run implying they literally gave up their lives and left everything to their luck.
