Just like the title states, what is the difference between multiple 12V rails and one?

I was under the impression that multiple rails isn't really a good thing compared to one strong rail, but everybody and their brother is slapping "next generation" and "multiple 12V rails" together in the same sentence.

What do I lose by going with a single rail system? What are the benefits? Cost/power consumption/stability/performance/upgrade possibilities... How are these impacted by multiple/single rails? In which ways (positive/negative)?

This might turn out to be some good information to sticky for the noobs that need help (such as myself, currently )