I think individual personality matters more than gender. That said, with the GCC's, females do tend to be a little more calm and cuddly, the males a little more nippy, hyper, and playful. The same likely holds true for crimson bellies but they are just not as common.
I remember when I got my GCC, at that time everything said males and females were the same - probably because they were less common then, and a fairly large percentage of owners didn't actually know their bird's sex. I would see people saying their GCC was so hyper it made their other birds nervous, or that it liked to lie on its back and wrestle fingers, and I wondered why mine was so different in personality - well those hyper ones were probably males. My Cheeky did wrestle with toys on her back a little as a baby, but outgrew it quickly.