I only have 1 child and I am not planning on having any more (due to my age plus medical reasons) but I can tell you from those I know with 2 kids, every family is different.
My hubby has 2 boys from his first marriage (now 16 and 17 - they are 13 months apart) and he will tell you that they were different from literally the moment they were born. Older one was quiet, laid-back, hardly ever cried. Younger one came out screaming and crying and has not stopped since. He is the sweetest most caring kid on the planet but he also wants attention non-stop and will be a total pain in the butt to get it. Now that he is 16 he is finally mellowing out a little bit but he would drive you crazy when he was younger.
My cousin now has 2 kids - a girl about to turn 3, and a baby boy born this past April. The girl is a sweetie pie but has always been more "high-maintenance" - whiny, clingy, sensitive, needs attention constantly. The baby boy is just a perpetually happy, content little love bug.
A good friend of ours has 3 girls. First 2 were wonderful - mature, cooperative, virtual clones of each other. The 3rd one is the "crazy one" - she's just more strong-willed and out-spoken.
So I don't know how much of it is birth order, gender, the parents, etc. But I do think eventually the law of averages catches up with you.