Why don't you just simply try it out? To download and install the software would be a first thing to do, I guess and a quite good companion to the LL video.
For a very quick description, I would say that C1 gives me a lot more control. When I moved over to C1, (I also came from LR), it didn't take me very long. Maybe, watching the LL video, takes longer, especially if you are not new to image editing, so that all the technical underlying aspects, are not new to you. I don't want to say that one shouldn't need to watch the LL video, on the contrary.
Sorry, others will have more detailed descriptions, I am sure.
BTW there are those who combine both in one workflow:
http://www.luminous-landscape.com/tutorial..._workflow.shtmlgood luck