I don't know that you're doing anything "wrong" so much as not understanding your son as much as your daughter. Does that make sense to you? And in not understanding him, you've had trouble bonding with him... just maybe. I'm NOT saying you don't love him as I'm certain that you adore him. Maybe right now you don't like him much... but I know you love him.
I could have written your post about my middle daughter when she was the same age. I wish someone had suggested to me that I have her evaluated much sooner than we did.
When she was in preschool we had her tested for lactose intolerance with a pediatric gastroenterologist after doing a successful elimination diet of all things milk, cream, cheese, whey, casein, etc. The elimination diet took a month. After the month, we gave her a glass of milk and the pain of gas, bloating, diarrhea, cramping intestines came back within an hour. She took a nitrogen breath test at the Gastro and we confirmed it for school purposes. But suddenly, after a few weeks of knowing what it felt like to feel good she had the words to tell us what was wrong. She had stopped so much crying because her bowels weren't betraying her. No more constipation AND diarrhea. It wasn't constant.
But we still had behaviors to worry about, that just minimized it. So we did another elimination diet of wheat/gluten. No difference. Then soy. No difference. Then high fructose corn syrup. Huge difference. Then red 40 food coloring. Huge difference. Same with other food dyes. We started the Feingold Diet. Big difference.
But we still had some behaviors to worry about, because all of that just minimized it. So we had her evaluated by a pediatric psychiatrist. Later, by a pediatric neurologist (two, actually). We were right about her having Sensory Integration Disorder (it used to be called Sensory Processing Disorder). You can read about it in "Raising A Sensory Smart Child" and "The Out Of Sync Child." Both are fantastic and easy reads, and if you see your child in them then it's a good chance he has sensory problems. They will help you relate to him in a big way.
It also turned out that she has ADD. In our case, her issues are all related to Autism Spectrum Disorder, but having sensory issues and gastric issues doesn't mean that ASD is a given. With my eldest daughter, she has some sensory issues as well and has ADHD and is highly sensitive to the food dyes and HFCS as well, but is fine in all other areas (she also has ODD, Oppositional Defiance).
So my main point is that your son's behavior issues very well could be dietary based. One reason I believe that is because it's been since birth. There's always a reason babies and young children cry. It's not how they're born. I don't believe that there's a default personality for being difficult in small children, especially when you're doing everything you know how to do as a parent and you've been trying to parent your son as well as you've been parenting your easy-going daughter.
I appreciate your efforts at being patient with him. I know he does too. It's not easy, and I've been there. I was there in the midst of having an older child like you, my difficult child, and then a newborn. It can get easier, and I'm hoping that if you go to a pediatric gastroenterologist who works with a pediatric nutritionist that you can start getting the help you need.