Should be a very large difference in the overall context of GPU performance.
Based on specs, the GPU in XB1 is around HD7770 level. HD7770 has 1.28Tflops of power over 1Ghz GPU @ 640 SPs, 16 ROPs, 72GB/sec memory bandwidth. The GPU in XB1 has about 1.31Tflops of power, clocked at ~850mhz and has 768 SPs, 16 ROPs, 68GB/sec memory bandwidth.
PS4 is actually slightly faster than HD7850 2GB. HD7850 has 1.761 Gflops of power over 860 mhz @ 1024 SPs, 32 ROPs, 154 GB/sec memory bandwidth. The GPU in PS4 supposedly has 1.84 Gflops of power over 800mhz @ 1152 SPs, 32 ROPs, 176GB/sec memory bandwidth.
With XB1's eDRAM, it might squeeze closer to HD7790 in performance.
Case 1: eDRAM is not efficiently used --> XB1 = HD7770
At 1080P no AA, HD7850 is
57% faster, with AA, 55% faster
http://www.computerbase.de/artikel/grafikkarten/2013/nvidia-geforce-gtx-770-im-test/4/
Case 2: eDRAM is used to push XB1 to HD7790 level of performance
At 1080P no AA, 7850 is 24% faster, 21% faster with AA
/snip