In my experience, it has everything to do with frequent, gentle handling, as well as hand feeding--starting as early in their lives as possible. Regardless of the breed or gender, that's the ticket. But you must be 100% consistent in order to build that perfect trust. And it's important to start as early as possible, so they grow up seeing us as friends, protectors and a source of all things wonderful.
We have five roosters, of different breeds, and 22 hens. Every single one of them is a sweetheart. Even the roosters are "lap chickens". We can handle any bird in our flock with no problem. Even if they are injured or sick, they trust us implicitly.
In our experience, such sweethearts are made, not born.
It's true that some breeds (buff orpingtons, for example) are more receptive and affectionate by nature. But we've yet to meet a bird of any breed that hasn't responded to consistent kindness, if started young. We even had one six-year-old wild rooster join our flock. When he first arrived, he was so scared of humans that he ran and hid.
It took us over a year, but now he's a lap chicken, too.
You can do it, too!