I'm in engineering, but I wouldn't necessarily say that one is better than the other. It really depends on what YOU want to do. There will always be a need for engineering... and it really depends on what KIND of engineering... because you have different fields like electrical engineering, mechanical engineering, chemical engineering, industrial engineering, civil engineering, material science engineering, etc.... And even WITHIN those kind of engineering are specialty fields. I went to school and studied Civll Engineering... however, within Civil Engineering, you have branches such as Transportation Planning, Traffic Engineering (which is what I am doing), Geotechnical Engineering, Environmental Engineering, Hydraulics Engineering, Structural Engineering... So the field of engineering is very diverse.... and within each of the types of engineering, you have specialty fields. To get my degree, I had to take classes in all of those branches/specialty fields of Civil Engineering. Then when I did my Masters, I branched out into Transportation.
Nursing... I do know that in the US there is a shortage of nurses and a great demand for them...
While it is good to know what fields are "hot", I wouldn't solely base my decision on it locking me into a particular field. You have to WANT to do it, be interested... not just do it for the money or just because there is a high demand for them.
Good luck in you decision. They are both very good fields into which to go. You can't really go wrong with either of them. It just depends on what YOU want to do.
The reason why I ended up in Traffic Engineering is because although I graduated with honors from college with a Civil Engineering degree, I didn't do so hot in the Geotehnical Engineering, Environmental Engineering, Material Science Engineering, Structural Engineering classes that I took. So I was limited really to Hydraulics or Traffic.... those were the two classes that I did well in...
If your concern is which is better for a particular gender.... I would let that be a determining factor either. I know lots of male nurses, I also know female engineers (I'm one :o) ) ... so it's really what you want to do. I chose my field because I have a high aptitude in math and like to figure out problems and innovative new solutions.