Not sure tbh. conqueror's Haki just increases the potency of what you have, while armament Haki gives you specific techniques.
Hardening:
Not only boosts your attack, but also acts as a defense, be it if your hardened body parts, like the fist, come into contact with lethal things, or as a means to protect yourself from incoming attacks, like Zoro protecting himself from King's explosion or Lucci blocking Zoro's slash.
Barrier/Flow:
An extension of hardening, which allows you to increase the AoE of your attacks and defense. It is also a crucial part of swordsmanship, as this flow effectively channeled through your blade allows you to cut through anything. I do not believe that conqueror's Haki can act here as a substitute. It's not confirmed that the barrier used in those attacks comes from CoC. The "no touch" thing is when two CoCs collide, while outside of it, pure CoC attacks had been seen making physical contact (like Kaido's blows that connected). When Luffy was hitting Kaido without touching him, he was combining CoC with CoA, so you cannot attribute it solely to CoC.
Internal Destruction:
The ability to bypass obstacles or ignore durability to damage the opponent from the inside out. That is not something achieved with CoC. Combining internal destruction CoA with CoC would allow you to add potency to those attacks.
And while CoC can interrupt DF abilities, I'm not sure a punch with nothing but CoC could bypass Logia intangibility. But even if it can, armament does have the 3 advantages mentioned above.