Whatever done in one will not transfer to the other, so no mixing between them. You have to choose in which you will work your render settings. By the looks of it, the Cycles Render is the better option because of its flexibility and rendering speed. So general what I want to know is there something that one does better than the other or generally, Cycles just has more in it?
Good question! Cycles specializes in accuracy at the cost of speed, while Blender Render specializes in speed at the cost of accuracy. At this point though, I wouldn't worry too much about Blender Render since it'll soon be replaced by Eevee. If you're ok with sticking to just Cycles for a bit beyond what you're learning in these courses, that would be my recommendation.