They are two separate models, and will most likely remain as such for the foreseeable future. While I can only speak for myself, I'd advocate using it because the language is indeed nice, and much more flexible overall than some of the alternatives. On top of that, it's got several large companies with a vested interest in its development, which is far more than can be said for some of its competition.
Really, the point I'd like to counter here is this: your productivity does not skyrocket, and it's not necessarily the reason to want to use JS server side. For example, the JS syntax works incredibly well for event based programming, and is largely tried and true with its use client side. That's a reason to want JS on the server, and I really wish people would quit throwing around the reusability claim like they do.
That alone makes it enough for me without its other benefits.
https://github.com/tmpvar/jsdom
jsdom implements DOM level 2 so you could actually mimic the javascript run in webpages (ie it would actually properly evaluate document.write() embedded in script tags). Web page scraping libraries in other languages won't have this feature easily because other languages will need to include a javascript interpreter along with their DOM emulator. I believe there's a java library out there that makes use of rhino to do this (htmlunit) but it took them quite some time to get there (several years). Most of the hard work in jsdom was implemented in a few months.