First, when people like us talk about console generations, average people say stuff like, "what the fuck are you talking about."
We're trying to scrunch all the consoles together while they see the Wii U as something a bit different. It's like the PS4 is the San Antonio Spurs, the Xbox One is the LA Lakers, and the Wii U is the Pittsburgh Xplosion from the CBA. While normal humans might talk about the Spurs vs. the Lakers, NO ONE is talking about the Spurs vs. the Pittsburgh Xplosion.
The Wii U has a mostly different assortment of games, it launched a year earlier, and it's named "Wii U". A console war with Nintendo? At the very most, the general public might see a "conflict". They don't know what goes on in the trenches, where console warriors like us go at it tooth and controller.
