You got some good answers in the comments, so I am summing that up here and adding a few comments of my own.
Torben nailed it in the comment:
Without going into the details you describe, keep in mind that all children are different. The other kid may be ahead right now but in half a year it can be other way round. Don't compare with others; there are a million factors that contribute to differences. Just look at each child separately. If your son is happy and healthy, that's great
For your specific issues:
Have you considered his hearing? A friend of mine had a 4 year old who had such a hard time communicating. They figured out she had reduced hearing (enough to react to loud noises and stuff, so they didn't discover it when she was a baby). It made it hard for her to hear how words were pronounced, so she had a hard time speaking. Some work with a speech therapist and hearing aid helped that - she has no issues now. You might want to check your son's hearing.
Some people are moody, and I also noticed that my 3.5 year old who generally has a sunny disposition is getting moody and whiney a lot more recently. I think it is a phase - he is discovering he can get moods, and how different things make him feel.
According to wikipedia, 10% of the population is left handed. From everyone I know who is left handed, do not force your son to use right hand, he is better of using his naturally dominant hand. Once he starts using scissors, be sure to get a left-handed one. Many other things comes in 'handedness', such as baseball gloves and more.
This seems totally normal to me. In fact, wanting to build different things is definitely a step ahead of my 3.5 year old, who hasn't totally understood the freedom of Lego yet. Getting angry when things don't go your way is very normal, I see this in all toddlers I have met :).
Seems normal. Some kids enjoy music more than others.
Your son may be right brain dominant, or he may not. He may just be developing differently than the neighbor's kid. As Torben said, don't compare.
Once he gets old enough to go to school, you can consider if there are other options than traditional 'sit at your desk' schools if you feel that wouldn't work for him. Homeschooling, Montessori, Waldorf, small classroom size schools might all be options, but I don't think you can rule out that he will do fine in a traditional school yet :).