If you think of lasers as what they are, the green spectrum is much more powerful than the red spectrum. Now think about the resources available, the Empire is a sprawling autocracy with massive resources available, versus the Republics lack of resources and necessary hand-me-down equipment. The empire is likely using more powerful equipment. Also, could just be that depending upon manufacturer, planet of origin, etc. different components are used.

As far as lightsabers go, I believe it's been explained.
For the empire!