Is there a best cavalier order?

Initially I thought 'order of the sword' ruled the roost. Then I noticed that as its all morale bonuses to hit and your banner gives you morale bonuses to hit (+1/4 per level if your a human with the cavalier favored class bonus. Its likely your charging about as a cavalier so it seems to double upfor limited return.
The 'order of the cockatrice' seems better as your bonus goes to damage (which banner doesn't work on).
Is there something I am missing, or when it comes tocavaliers are the black knight/green knight types that serve themselves cooler and mechanically better?

I don't know that I'd say there's a single best order, but there are several good ones. One thing to bear in mind is that the challenge bonus is only a small part of what each Order has to offer.

The Cavalier Guide has a pretty good breakdown of the good and bad on each order. Really, which one's best boils down to what you want out of the Cavalier.

It really boils down to the party composition and rest of the build.

Order Of The Cockatrice challenge ability is less useful when there are other melee-oriented party members when Order Of The Dragon cavalier will be the best. Also, cockatrices 8th level ability does not synergize with their challenge ability.

Order Of The Sword challenge ability may not stack with the banner, but it works outside of charge and personally, I prefer 2nd level and 8th level abilities to those offered by O.o.T.C.

I consider Order of the Dragon the best one, in the long term.

Ronin / Knight Errant has a very nice level 2 ability, if you're just dipping.

IIRC, Order of the Sword is best for a mounted archery build due to how its challenge bonus works or something.

I consider Order of the Dragon the best one, in the long term.

Dragon has a lot going for it. I'd say that while other orders can beat it if you've got a specific build in mind (Sword is best for pure mounted combat, Cockatrice for Performance Combat, Seal for including combat maneuvers, etc) the Order of the Dragon is the best general-purpose order. It also helps that it's got one of the simpler edicts; in most campaigns, "support the rest of your party" isn't going to be an issue.

Enforcer and Bludgeoner works well with Cockatrice,and the theme fits a non lance sort of warrior.

As samurai you can get cavalier orders does it state anywhere i missed the reverse applies?

Yeah, then entry in Ultimate Combat specifies that Samurai Orders can be taken by Cavaliers as well.