To somebody who has never been there, the names probably have no significance besides the fact that they're names.
nothing a quick google couldn't solve...they are 2 of the busiest, dirtiest, most overpriced locations in Japan
Kabukicho is good for nights out though (and a huge amount of arcades if you like playing video games?) - my company offices are in Nishi Shinjuku so we head there quite often
I would choose the second over the first, but would probably like to stay a few stops away in a cheaper and bigger hotel. I stayed at a place in Ueno which was pretty nice and had nice big rooms (and a pool and gym) a few years back.