Pros: friendly, docile, calm, make great mothers, good for picking up and cuddling, comes in a variety of colors
Cons: can't get wet, gets broody for long periods, easily gets dirty vent, is more prone to lice and mites, get bullied by more aggressive breeds
A few years ago my family and I owned a small flock of these as chicks and eventually we mixed them with another small flock of belgian d'uccles. We preferred bantams because they didn't seem to wander into the neighbors' yards. Over time though some of them died (one got eaten by a neighbor's dog, one got sick and one died on the brood), and now I only have one left. She's an old girl and has retired from egg laying. I can make the following points from my experiences with cochins.
They are a very calm, very docile breed. Once they get used to being handled, they won't mind it too much. Their friendly disposition allows them to be mixed with other docile breeds, but be aware, put them with a more aggressive breed of chicken and they will quickly be overtaken in the pecking order. They can't hold their own position against a chicken that will fight them, especially if the chicken is bigger and/or faster than they are. If the aggressive chicken becomes a bully the cochin will be forced into hiding and won't come out to eat or drink. You have to protect them. They're not very fast (well compared to other breeds) and will most likely be eaten by predators.
I believe the main reason people will want this breed is because it's fluffy. Who doesn't want to hug a fluffy chicken? However, the fluffiness of the chicken presents its own set of problems. First of all, the feathers trap heat, so the chicken does not cope well in hot weather (especially if it's a black one). On a hot day you may find it hiding under trees all day. The sheer amount of feathers on the chicken also provide great hiding places for lice and mites. You may discover the cochin gets infested more often than other breeds. It may also get really dirty more often. There's a condition that is shared among all chicken breeds called "dirty poo butt" (at least that's what I think it's called) where feces get trapped in the rear feathers of the chicken. After a while it builds up and the chicken starts to smell. Bear in mind this doesn't happen with ALL cochin bantams (or all chickens in general), but it has happened with one or two of mine. It simply means you may have to either give them a warm soapy bath every fortnight or trim their rear feathers. Every now and then I find myself examining my girl's vent to see if she needs a bath. Speaking of baths, this breed is similar to the silkie, in the fact that the feathers are NOT waterproof. If the cochin gets wet (in the rain or by accident), it can easily get a chill. So your yard/coop needs places for it to get out of the rain and stay dry. If you're giving one a bath, make sure you completely dry it off with a hair dryer.
I've experienced that the cochin gets VERY broody in the Summer and will sit on a nest for about a month, even if the eggs there don't hatch. We were fortunate enough to get a fertile egg and have our cochin hatch it. She made an excellent mother. Very dedicated and protective of her young. We've had cochins get broody before this however. One of them got so broody that she wouldn't get up to eat or drink (we even put the food and water right next to the nest). She eventually died on the brood. When they're not broody, they won't lay often (usually they lay a stockpile of eggs and then get broody on them). They will stop laying in the Winter when the weather turns cold. I remember mine laid about once every few days. The eggs were small, white and round. The cochin is not a good breed for egg production.
So in short, the cochin is very friendly and will make a great pet, but must be protected against predators and bully chickens. Their fluffy bodies may require routine maintenance and need to stay dry. They get broody for long periods and don't lay often but make great mothers for breeding.