Holy shit, those idiots over at Digital Foundry have really fucked up this conversation, haven't they?
To preface this post I want to say that although I admire what Digital Foundry tried to do but their methodologies were not only flawed but straight up wrong.
The first thing they did wrong was select the wrong graphics cards to correctly compare the 2 situations.
For the Xbox One they used a HD 7850 over a HD 7790 while for the PS4 they used a 7870 XT over a 7850. This is wrong because using the 7850 for the Xbox One thrusts it into a whole different category of graphics cards that bring many advantages not present in the Xbox One GPU (32 ROPs vs 16 ROPs).
The methodology they used would have been perfect if they grabbed a HD 7790 and clocked it to ~731 Mhz for the Xbox One's GPU and used a a HD 7850 and clocked it to 898 Mhz.
Xbox One = 1.310 Teraflops ------- (HD 7790)Bonaire @ 731 Mhz = .731*2*896 = ~1.310 Teraflops
PS4 = 1.84 Teraflops ------- (HD 7850)Pitcairn @ 898 Mhz = .898*2*1024 = ~1.84 Teraflops
I reckon using these cards at these clocks would really show the GPU difference between the two consoles but alas Digital Foundry went about this some other dumbass way.
To get to the point since I don't have the hardware I mentioned above on hand to conduct the tests myself but I can extrapolate data from graphics cards that are similar to what goes into these consoles. For the Xbox One that would be an HD 7770 because it has a similar amount of GPU power as the GPU used in the Xbox One (1.310 Tflops vs 1.28 Tflops) while for the PS4 I would use the HD 7850 (1.84 Tflops vs 1.76 Tflops) and then compare the results for a realistic look at the performance gap. Oh, by the way the gap between 1.28(HD 7770) and 1.76(HD 7850) is smaller than the gap between 1.31(Xbox One) and 1.84(PS4) so that's already giving a slight break to the Xbox One in this comparison.
For my analysis I am using benchmark numbers from Anandtech.com:
http://anandtech.com/bench/product/777?vs=778
Using the data above I came up with the following chart:
I submit to you that the performance difference between the Xbox One and the PS4 will be much more apparent than what Digital Foundry has hypothesized and that the overall difference in power will not only be tangible but possible even staggering.