"Sources close to the project" are offering a ballpark figure of a six times performance increase over the Xbox 360, or 20 percent more power than the Wii U, though this doesn't really tell us anything in real terms.
It's an understatement to say "this doesn't really tell us anything in real terms". It actually doesn't tell us anything in any terms at all. We don't actually know how powerful the Wii U is for sure (though people have reasonable beginnings to guesses). What we do know, though, is that the numbers in that sentence are ridiculous.
A "six times performance increase" means the new Xbox would have 7x the performance of the Xbox 360. That's fine and dandy, though it doesn't really tell us anything that matters. "20 percent more power than the Wii U" equates to 120% the Wii U's performance, or 1.2x the Wii U. Hrumph. Let's do some simple algebra:
1.2 x Wii U = 7 x Xbox 360
Wii U = 7/1.2 x Xbox 360
Wii U = 5.833... x Xbox 360
Are you really trying to tell me the Wii U is nearly 6 times as powerful as the Xbox 360? Because that's a whole lot of nonsense. (Even as a very big fan of Nintendo, I can't fool myself into believing the Wii U graphical demos have illustrated anything more than a marginal increase in graphical computing power over the Xbox 360 and PS3.)
Now that we've gotten the nonsense out of the way, there is a little bit of concrete information that does tell us something if true:
IGN is reporting that the next Xbox will ship in autumn 2013, with a GPU based on AMD's 40nm Radeon 6000 architecture and allegedly offering performance akin to the Radeon HD 6670 from last year.
If true, this tells us Microsoft isn't going to put out a system nearly as graphically powerful for its time as it did with the Xbox 360. That said, there were many technical design choices in the 360 that gave it performance advantages to comparable PC hardware (10MB on-die eDRAM, unified system and graphics memory, etc.).
Sony and Microsoft both know they can't afford to loss lead in the next generation the way they did this time around. They'll likely have to keep core architecture compatibility with their previous systems because of the enormous platforms Xbox Live and PlayStation Network (and their downloadable games) have become. If one of the companies abandons all the downloadable titles from the previous generation and the other doesn't, that'll be a huge knock.
Both Sony and Microsoft will have to improve performance affordably while keeping processing component costs down because much more of their costs will come from controller/input R&D and bundling (Kinect/Move, etc.). Nintendo changed what people expect of new consoles, for better or worse, and now Microsoft and Sony have to play this new game.