Aerdan I agree with most of your post but it did not dominate the generation as much as you say it did: http://gematsu.com/2013/11/worldwide-playstation-3-sales-reach-80-millionhttp://www.ign.com/articles/2013/10/17/xbox-360-80-million-sold-and-countinghttp://www.nintendo.co.jp/ir/library/historical_data/pdf/consolidated_sales_e1309.pdf
At first it did no question, but that's old news, outdated by years now.
Really, I'd argue there was no single winner, as most of Nintendo's sales were in two groups: 1. Diehard Nintendo Fans, of which there are an insane amount. 2. "New" fans that don't normally play a lot of games. Much of the standard gamer market which gamed on the GC's 3rd party games migrated to PS3 and X360.
The profitability question is also a bit muddled. The PS3 and X360 sold initially at a loss, the PS3 very much so due to the blu-ray drive of financial doom, but they eventually got the costs down, and had a huge amount of successful third party games alongside of their first party games. Nintendo did not have nearly as many third party games that sold hugely, but they had lower developmental costs both in terms of the future hardware and in terms of their own games. Plus, until the 3DS price cut, they had never sold a console at a loss before, so the Wii's base hardware made them a fuckton of cash.
Nintendo also did not jump on the Online Games bandwagon nearly as much as Sony and MS did. A large reason why WiiWare failed was the 60 or so MB limit it had, and it was never really pushed. Virtual Console on the other hand, made a lot of money but I don't think any public figures have been announced as to how much they made from it. PSN Store and XBLA sold a far, far higher amount of games, but they were, for the most part, not as profitable per sale as the VC ones were.
In addition to all of that, we don't know how much money the various video/music services and MS/Sony's outright selling of videos and music made them. Or, more importantly, how that was counted on their balance sheets.
Those might not be listed under the video gaming portion of their list of corporate profits, I don't know. I don't really know where to look over than their SEC filings, and even then there's so much paper to look through there it'd take me ages.
Combine all of that with the fact that all these consoles are still selling, and who the fuck knows which of the three won the console war of last gen.
All we really know is that Nintendo made a fuckton of cash, Sony's gaming division lost a fuckton and then made a fuckton, and MS' gaming division almost entirely lost a fuckton.