Caveat, I am no horse enby, so folks, come in and poke me if I'm being grossly inaccurate.
1: With two legs, a chocobo can't buck like a horse can. To unseat a rider it's going to have to try other things.
2: A rider with long enough legs will probably hook them over the fold of the wing joint and over the thigh muscles, to help retain a seated position. Concept art of chocobo saddles implies so.
3: The back feathers of a chocobo may be softer and downier, and therefore able to take the pressure of a saddle and pad without having their quill structure crushed. Nevertheless sores might be more problematic on a chocobo with a badly distributed load than on a horse because feathers are more easily ripped out than smooth horse hair.
4: Because chocobos only have two legs, laming one is a Very Big Problem. I don't imagine they live too long without swift healing magic and possible splinting and other care.
5: While the game doesn't render the wearer's feet in stirrups I imagine they're a necessity. Especially in flight. I imagine flight saddles have an additional strap to keep the rider in if anything happens, like turbulent winds, etc, like military saddles do.
6: I've noticed that riders sit further forward on a chocobo than they might on a horse, but then chocobos don't have front legs, just wings. The weight of the rider is placed over where the shoulders on a horse would be, which is incidentally how bareback equestrians sit.
7: HOW DO YOU GUIDE THE DANG BIRD. Horses are guided with the pressure of the bit in the mouth. Chocobo tack does not have a bit. One imagines that most riding chocobos are actually trained to obey dressage-like cues and can be guided almost exclusively with the knees.
8: Chocobos seem to be eaters of herbage as opposed to grazers of grass, like ungulates. Without teeth, they probably seek out pebbles and stones to eat as gastroliths to help grind food in the gizzard.
Chocobos may not need as much watering as horses due to the fact that they eat high-moisture, juicy vegetables and fruits along with their customary diet of herbage.
9: Sustaining chocobos on voyage may therefore be a bit easier than sustaining horses on voyage, as long as your turnips and beets and mangel-wurzels don't spoil.
10: Bird manure is generally too "hot" to be used on crops from scratch. But well-mixed with plant matter (scraps from the chocobos' own feed bowls, stall straw) it will compost down into a rich soil amendment.
Chocobo grooms probably make a good side profit in aged compost.
11: Horses get horse shoes. Racing chocobos get spur-like foot harnesses to improve grip on race tracks.
But the bottom of a chocobo's large foot is a large surface area to protect and treat in the case of difficult terrain and you can't give chocobos horse shoes. To that end, I imagine riders in rougher terrain, like the salt loch in Gyr Abania, actually put oiled leather booties on their chocobos' feet to prevent say, hypersaline grit from building up in the wrinkles and crevices of their toes, and causing sores.
12: Salts and other essential minerals are mixed into horse feed, and salt blocks are put out for pastured livestock, to let them meet their mineral needs. I actually imagine chocobokeeps putting crushed cuttlebone in chocobo feed, to get them supplemented with extra calcium.
These are all thoughts I've had playing my gunbreaker through HW, SB, and ShB. Cross-posted to my personal Twitter.