I see a lot of so called spec comparison on places like Neogaf that are incomplete, or extremely biased towards PS4 to the point of being nonsense, so I wanted make a true, unbiased reference. The PS4 will go second and be compared to the X1 baseline in terms of percentages.
Disc: 6X Blu Ray
Disc capacity: 50 GB
HDD: 500 GB 5400 RPM
RAM quantity: 8GB
CPU: 8 core (6 game usable) 1.75 ghz Jaguar (Plus SHAPE audio chip likely ~1 CPU core of audio processing, +cloud support which we will ignore for now but could offload things like AI from X1 CPU in the future)
GPU FLOPS 1.31 teraflops
Texture units 48 at 853 mhz
Triangle setup engines: 2 at 853 mhz
ROPS 16 at 853 mhz
Peak bandwidth: 204+68=272 GB/s
Peak BW per GFLOP= 272,000 MB/S/1310=207.6 MB/S/GFLOP
Disc: 6X Blu Ray (+0%)
Disc capacity: 50 GB (+0%)
HDD 500GB 5400 RPM (+0%)
RAM quantity: 8GB (+0%)
CPU 8 core (6 game usable) Jaguar CPU 1.6 ghz (-9% raw, -24% after removing 1 core for audio processing to match SHAPE, ignoring X1's cloud capability for now)
GPU FLOPS: 1.843 (+41%)
Texture units: 72 at 800 mhz (+41%)
Triangle setup engines: 2 at 800 mhz (-7%)
ROPS: 32 at 800 mhz (+88%) (However, the real world impact will be much lower as 16 ROPS typically enough at 1080P and less)
Peak bandwidth: 176 GB/s (-35%)
Peak BW per GFLOP: 176,000 MB/S/1843=95.5 MB/S/GFLOP (-54%)
Specs PS4 is superior in: ROPS (+88%), GFLOPS (+41%) Texture Units (+41%)
Specs X1 is superior in: CPU (+9%) Geometry setup (+7%) Peak bandwith + (55%) Peak BW per GFLOP (+117%)
Specs they are equal in: Ram capacity, Optical Disc capacity, Optical disc read speed, Hard drive read speed.
There you have the complete picture of baseline specs, subject to countless other variables we know nothing about...
From a high level, PS4 has a stronger GPU while X1 has a sigjnificant edge in peak bandwidth, and a slight to moderate advantage in CPU, which could grow if developers begin to leverage the cloud in the future. The disc read subystems and RAM quantities are identical.