Listed below is the most up-to-date information (based on last edited date in title) for the known consoles coming out 2012 and 2013.

Sources linked below this first chart.

DON'T MISS MY SECOND POST WITH CPU AND GPU COMPARISONS

Wii U Confirmed and Official Specs:
Nintendo site for overall information - http://www.nintendo.com/wiiu/features/tech-specs/
NeoGAF for detailed CPU - http://www.neogaf.com/forum/showthread.php?t=513471
NeoGAF for detailed GPU - http://www.neogaf.com/forum/showthread.php?t=511628

PS4 Confirmed & Official Specs:
Sony specs (PS4/DS4/Eye4) - http://us.playstation.com/ps4/features/techspecs/
NO DRM - http://www.ign.com/articles/2013/06/11/e3-2013-playstation-4-supports-used-games-dont-require-online-connection
Good general info on the PS4 CPU -
http://www.techpowerup.com/180394/AMD-quot-Jaguar-quot-Micro-architecture-Takes-the-Fight-to-Atom-with-AVX-SSE4-Quad-Core.html
Sources for PS4 RAM allocation - http://www.eurogamer.net/articles/digitalfoundry-ps3-system-software-memory
GPU teardown - http://www.extremetech.com/extreme/171375-reverse-engineered-ps4-apu-reveals-the-consoles-real-cpu-and-gpu-specs

Xbox One Confirmed & Offical Specs: 
Basic specs and overview by MS - http://www.xbox.com/en-US/xboxone/what-it-is
DRM policies - http://news.xbox.com/2013/06/license (DRM has now been removed. Will work same as X360 for physical discs)
Source for DRM removal - http://news.xbox.com/2013/06/update
Wired article on a lot of info - http://www.wired.com/gadgetlab/2013/05/xbox-one
GAF thread with screen grab of specs - http://www.neogaf.com/forum/showthread.php?t=560464
6 CPU cores and 5GB ram for gaming - http://kotaku.com/the-five-possible-states-of-xbox-one-games-are-strangel-509597078
Good general  info on the XBOne CPU - http://www.techpowerup.com/180394/AMD-quot-Jaguar-quot-Micro-architecture-Takes-the-Fight-to-Atom-with-AVX-SSE4-Quad-Core.html
Major Nelson  on increased GPU clock - http://majornelson.com/cast/2013/08/02/mnr-486-marc-whitten-updates-us-on-the-progress-of-xbox-one/

Other major comparisons:
http://www.anandtech.com/show/6972/xbox-one-hardware-compared-to-playstation-4
http://www.ign.com/wikis/xbox-one/PS4_vs._Xbox_One_vs._Wii_U_Comparison_Chart

CPU: (neXtBox ~ PS4 >> Wii U)

With WiiU finally being torn down and evidently hacked, the CPU is clear now. It is an enhanced Wii CPU. The clock is about twice as fast PER CORE and it has THREE cores vs Wii's ONE core. Along with that comes 12-times the cache. As compared to what is likely in the other next gen systems... clearly it will be below them by a significant amount.

MSony are essentially going to provide the same CPU within their overall APU design. However, this will not mean they are identical as each company will have tweaked various other items related to memory, bandwidth, etc.

However in the end, it appears we'll see a MSony CPU that is basically the same while WiiU lags far behind. Considering we're approaching a point where the GPU will be doing nearly all the work, this may not be as big of an issue for WiiU as it suggests.

For CPUs we're looking at: XBox 360 * 1.5 = WiiU * 4 = neXtBox ~ PS4.

GPU: (PS4 > neXtBox >> Wii U)

Nintendo has gone with a 100% custom chip design in order for them to create their MCM solution with a strong focus on efficiency and backwards compatibility. The end result is a design that is not like any standard AMD GPU, making it difficult to analyze. It does contain fast eDRAM (32MB + 2MB) and SRAM (1MB). Statements support the idea that it will utilize the same DX11 type features and technologies as its competitors, but it will be hampered by a far slower GPU and memory bandwidth.

MS appears to be going with a slightly smaller GPU (as compared with Sony) along with a slower memory pipeline and some sort of "Move Engine" that is believed to assist its data transfer speeds within the APU. It will go with general DD3 RAM and compliment that with 32MB of eSRAM. Being a Microsoft product, it will be utilizing 11.x varient of DirectX.

Sony is going with a more traditional PC-like approach in that its matching the GPU with actual GDDR5 RAM vs general purpose DDR3 RAM. It has 18 compute units (CU) in its southern islands based GPU. Like WiiU, this will be support DX11 type features and technologies. [PS4 GPU: 1.84 TFLOPS, Engine Clock 800Mhz, 18 Compute Units (1152 Stream Processors), 72 Texture Units , 8GB GDDR5 with 176.0GB/s memory bandwidth (shared with CPU) ]

For GPUs we're looking at: XBox 360 * 1.5 = WiiU * 6 = neXtBox * 1.5 = PS4.

Memory: (PS4 > neXtBox >> Wii U)

This means that Sony has a clear advantage in RAM due to speed even when including the benefits of embedded ram on WiiU/XOne's GPUs. XOne will be closest with similar overall storage capabilities but slower transfer rates while Wii U will be both far smaller and slower than both of its competitors. These differences are attempted to be included in the comparisons above for CPU/GPU.

Controls:

Were there any rumors about the WiiU coming with a harddrive? I remember the rumor about it having 8 GB internal storage, but no other storage-related rumors.

For those of us who know nothing of these things: IF these rumours are true, how much more powerful than Wii U will the next Xbox be?

Not really enough information to say either way, especially when you consider that all hardware listed will (likely) be heavily modified/customized to operate under the performance, heat and cost requirements of each of the manufacturers.

Absolutely true. My initial comparisons are just based off standard specs and generalizations.

http://wiiuupdates.com/wp-content/uploads/2011/06/i3vXP.jpg

It's the size of the die that the CPU is on. The smaller the size the more efficient the CPU meaning it uses less power, produces less heat, etc. Over time one big contributor to reduced console size and cost is due to the reduction of the CPU and GPU sizes.

As HappySqurriel said, it's impossible so say anything definitive from what we see here. The Xbox looks like it may command a more or less noticable advantage in terms of the CPU and RAM, but they're still so close that the GPUs will be the determining factor in most comparisons I imagine. And there is nowhere near enough information about the GPUs to compare them, so it's still up in the air.

Ok, we'll just have to wait and see then. Thank you!