Using full sentences and punctuation.
Like seriously... 9 Words plus a question mark is a little bit lazy, dont you think?
However, to the topic:
I guess CoA Haki as defense is much better because it, as far as i think it works, can protect you from elemental Logia powers.
To be honest I don't think the comparison between them is entirely relevant. I get that comparing them is possible but given how each seems to work the comparison is moot because even if they can have potentially similar functions the two of them have different scopes.
Haki as a defense has been shown by rayleigh and the boa sisters at large. In those cases the attackers did not even physically reach the targets. Of course they were scenarios of haki vs no haki so to speak so the things being that extreme makes sense. In haki vs haki fights it seems like contact is more than normal at large so perhaps the situation is that haki and haki kinda cancel each other out. I guess damage would depend on the strength of the haki in question.
So then we have tekkai. Much less scope than haki but highly specific in its use. Tekkai simply somehow hardens your skin. It has been shown to be able to resist physical threats easily although enough strength can get past it (although the same can be said for haki based on what we saw between luffy and the boa sisters).
So how do they compare.... they act under different scopes and different rules so no clue. Haki is not in itself a martial art or fighting style. Rokushiki is. Haki is something inherent in all humans, it is not meant to replace or be compared to martial arts or DF. haki is a complement to both of those. In this particular case I would argue rokushiki in particular is meant specifically to work in perfect synergy with haki. It is a type of martial arts designed to make full use of all the practical uses of haki. Each and every technique rokushiki has can be significantly enhanced via haki, perhaps more so than just normal martial arts at large.
Thinking about it. Shigan and tekkai would benefit particularly well from armor haki, in particular armor hardening. Just fingers can be as powerful as bullets. Add in haki and you get cannons. With tekkai and hardened haki you get perhaps synergy between two independent forms of hardening. Its as resistant as a human body can be without a df. Of course if you add in a DF in the mix you have something worth fearing. Imagine jozu with tekkai and hardened haki. Its brutal.
Ok, when it comes to soru and geppou I am unsure of how it would work however cases can still be made. Soru is a high speed movement technique, perhaps observation haki can increase your awareness of your surroundings to further increase its efficiency. Perhaps having haki in your legs can increase the speed considering soru is supposed to work by kicking the ground a number of times really fast. Geppou can perhaps be improved in a similar manner via observation haki and armor haki would perhaps allow a better foothold. Armor haki helps when touching intangible so perhaps the use of gepou can be improved via it. Perhaps even a combination between soru and geppou is possible if haki does help improve contact.
Kami-e can easily be improved significantly via observation haki. We have seen characters easily dodge with it and kamie is a particularly good skill for dodging. Observation haki and kamie together could help perform seemingly improbable or impossible dodges.
Rankyaku probably works in a similar manner to standard swordsmanship. Zoro was able to cut monet from a distance with haki so it makes sense the same could be done with rankyaku.
Anyways, I guess my point is that I am altogether iffy about comparing martial arts and haki. They are not the same thing, haki alone without it working in synergy with something is esentially useless. Haki is meant to enhance martial arts and fruit abilities, not replace them. Even if you take cases from the manga showcasing this the issue probably won't be a matter of which is better but rather which character was stronger to begin with.
this does bring up the thought....
what if someone could do BOTH
i beleive that would be an epic combination
Anywho, this is a damn good question. kkck probably hit the nail on the head though in that Rokushiki may have been developed to maximize the potential of haki. I can also see Rokushiki as a way to "mass produce" strong marines who aren't adept in haki. If you can't master the spiritual aspect, you can master the physical. But because of that, there are some flaws. Tekkai doesn't allow you to move freely, Shigan, while strong, still has a chance to backfire if used incorrectly and can't be used to counter attack, etc. You have the quantity, but quality users may be far and few.
I'm not sure as both are useful and have their drawbacks. Tekkai makes one nearly invulnerable to physical attacks, but what if logia power is involved, like Akainu's magma or Whitebeard's guro guro no mi? Armament haki can protect against most physical attacks and logia attacks, as well as allow one to damage a logia or paramecia user. All things considered, it seems Color of Armament haki seems to be better because it offers more benefit than tekkai.
I honestly think tekkai is lighter form of armament haki.
I've also always had the impression that although Rokushiki was introduced way back in Water 7 as sort of a mystical-yet-trainable Marine martial arts style, it is just a variation on using the different types of Haki. That is to say, I believe Oda had this concept of a power to influence physical and mental capabilities of the user when he started out (e.g. Shanks scaring the Sea Monster that got his arm) but he decided to drop some examples (e.g. Rokushiki) before he laid down the public framework for Haki itself.
It's a cool (and widely used) trick in shounen story-telling to first introduce a bizarre and abstract power-related concept and then explain it quite systematically, making it seem more realistic and attainable. It helps tie different elements of the story together retroactively. Who knows, one day we might get some more elaboration on the origin of Haki.
And I believe the visual difference between "Tekkai" (hardening with Armament Haki) and "Armament Haki" (imaginary armor with a "blast radius" when used offensively; e.g. by Sentoumaru or Rayleigh) has also been illustrated by Luffy to be different uses of the same source of power. Both serve defensive and offensive purposes, it remains to be seen if Oda decides to go into such detail that a difference in utility emerges between the two.