I'm an electrical engineer and worked as a project lead at my previous job. We developed industrial products for the oil and gas industry.
Part of my job was hiring and building a team of electrical, software, and mechanical engineers. I can tell you that the hardest position to fill for was electrical engineering. Mechanical engineers were a dime a dozen, and we easily had our pick from a group of great candidates. Their pay range was also lower. Software engineers can be difficult to find as well, but there are many out there who are passionate and could fill the role we needed. Software engineers commanded the highest salary. Appropriate electrical engineers were just hard to find. When I graduated in December 2007, I was one of two electrical engineers graduating with a BS at a University of 12,000 students. I've spent more time looking for electrical engineers than any other discipline.
As far as schools, I've had good experiences with all types of engineers from all types of schools, BUT the best engineer I've ever worked with had a BS degree from Northwestern. He was probably a sharp student before attending that school, but I'm sure the caliber of school helped.