Please help noob understand how MP's effect sharpness.

I keep reading posts regarding D800 vs D700. Some say the NR on the D800 isn't as good or that it may not be as sharp because it has 36 MP's instead of 12. Then some people will say that if you downsize the D800 photo to 12 mp the NR and the sharpness will be as good or better then the D700. When they say downsize do they mean in your software take the resolution down, or in camera set it to a lower resolution?