Trying to decide on a mounted martial character for a Kingmaker Campaign I'm joining and I'm torn between these two. I like the bonuses and flavour of the Cavalier (especial Wild Shape your mount for Order of the Beast) but can't help but feel with the number of feats I need to make mounted combat effective he won't be very good off his horse.
So looking for recommendations straight Cavalier or Dragoon 16(15)/Cavalier 4(5) for the Mount, Expert Trainer, and Horse Master (possibly Banner).
There is a big difference between being effective and being an expert. You can be quite effective in a combat style without being the best there is. All you need to be effective is to be able to defeat your enemies. For mounted combat all you really need is a mount, a decent ride skill and proper equipment. Since the cavalier gets an animal companion level mount, and has ride as a class skill he is good to go.
I have seen this attitude come up a lot and not just in regards to mounted combat. Many characters feel that if they are not the best at something they don’t want to bother with it. I knew one player who was playing a melee focused paladin and did not even bother with a ranged weapon. I suggested he pick up a bow and his response was I don’t know how to use a bow. While we did have a archery based ranger in the group that was a lot better than he was, he still had proficiency with the bow.
A Gendarme nixes the tactician ability to gain the mounted combat feats for free basically, and the Order of the Sword also grants another one for free at 8th level, as well as the ability to add your mount's STR to your damage rolls when charging.
Other than that, more feats to be effective off-mount are the same kind of feats you want while mounted, Power Attack, Weapon Focus, etc.
You may want to pick up a secondary weapon to use while not mounted, in case you want more typical optimized damage output like a nodachi or a falchion.
If you want to really mix up your combat styles, then go Ranger, and use your animal companion as a mount. You can pick up some archery feats with your combat style by bypassing the heavy prerequisites and spend your regular feats on Power Attack and some mounted options.
Ok, so first off you should know that you will only hit 17th level by the end of Kingmaker, so you have a few less levels to work with than you thought.
So the Cavalier build that seems to show up a decent bit is a Gendarme with Order of the Sword (as master_marshmallow pointed out). This builds to a pretty nasty mounted charger. Good levels to cut it off are at 4th, 5th and 8th. 4th for Expert Trainer (and therefore Horse Master), 5th for a bonus feat and banner, 8th for a bonus feat and the ability to add your mount's Strength on charge attacks.
Dragoon provides a lot of feats, not just for mounted combat but also enough to be decent when not mounted. Remember, you can use a lance when unmounted, it is just a two handed weapon. Good cut off levels are 5th, 7th, and 9th. 5th for sweet spear training (compatible with Gloves of Dueling), 7th for the ability to strike adjacent with your lance, 9th for an increase in spear training and the ability to stack you banner with cavalier.
Personally, I would go Fighter 9, Cavalier 8, alternating every other level, with a "capstone" of Fighter 9 granting +1 to hit and damage with lances, +2 to saves vs fear/attacks made on a charge.
See also magic items like Champions Banner and Sash of the War Champion.