Who would win a war between North Korea and South Korea?

My opinion is South Korea because of the support of the United States military. I think if North Korea invaded the south, they would make progress for a short time, as in the Korean War, and then they would lose by no air support, supplies, ect. The US would bomb the hell out of all their Navy bases and Air bases. I think on the situation now, if China stayed out of it, and the North was all alone against the United Nations, they wouldn't have a chance and would lose pretty quickly. Their military morale would be a factor as well. I don't think their missile guidence systems are good enough to hit with accuracy. They could aim a nuclear missile towards Hawaii and hit Russia or China accidently or themselves.