The Xbox 360 and the PS3 were reasonably powerful, almost as good as a good PC in 2006.
These next gen machines are outdone by my one year old 800$ build...
The difference is that your $800 PC is static. It will never get better over time, the graphics will always be stuck at the same level as the day you bought it. While newer and newer games are released, you will find yourself having to turn down graphic settings, making each new game require lower and lower settings to keep the same frame rates, eventually the newest games won't be possible on the static $800 hardware.
However, a game console will actually get better over time. It's dynamic. Because it's a closed system developers get to tweak their code for every new game, getting more/better performance for each new release. This is because game consoles can be fully optimized by game developers, seeing as they know exactly what kind of hardware and drivers are in every single Xbox One. Not to mention, the game console is using FAR less resources to accomplish the same goals as a generic $800 PC.
Just look at the graphics between Halo 3 (right) and Halo 4 (left). Both on console, developed 5 years apart.
Full Disclosure: I own 2 gaming PC's, both custom built by me for over $1,200 each (at the time parts were purchased). PC 1: Intel Core i5, GTX 570, 8GB DDR3. PC 2: Intel Core i7, GTX 670, 16GB DDR3.
I know full well how much it costs to keep a gaming PC relevant for games.