According to Eurogamer, the next generation gaming console from Sony and Microsoft will be running on an AMD Jaguar platform, which affords them both a super powerful eight-core CPU pushing 1.6GHz. As for the graphics card, the article suggests the PS4 could have graphic performances somewhere along the line of the AMD Radeon 7970M. No word on what the Xbox 720 is expected to be pushing, but it should be some where in that ball park.
There have been a few rumors flying around suggesting the PS4 could be a bit more powerful than the Xbox (which was always the cause with the PS3 vs. Xbox 360,) but some rumored reports on amount of RAM each console will be sporting could offset any advantage the PS4 may have. The PS4 could come with 4GB of ram, while the Xbox 720 could be running up to 8GB.
Just so you know, PS4 and Xbox 720 are not the official names for these consoles, neither are these rumored specs confirmed, but it sure is fun to get excited early on.
Check out the video below showing off the graphic capabilities of the mentioned AMD Radeon 7970M. Keep in mind, the demos are running current generation titles, so its hard to judge what the future will bring, but even on current generation titles, the Radeon 7970M offers some amazing performance.