It appears from what we know that the PS4 has a bit of an edge in terms of graphics/compute power, and its probably going to be favored by spec-monkeys, but the XBox One is close enough in terms of hardware capability that the system software, XBox Live / Cloud infrastructure, and general integration with Windows PC / Windows service ecosystem could very easliy close the appeal gap for most people.
We got some specs and numbers to compare -- The Xbox One has 768 graphics compute units vs. 896 (+ 256 for compute only) in the PS4, both are DX11.1+ feature set, 8GB DDR3 + 32MB ESRAM vs 8GB GDDR5, and both are now confirmed to use 8 "jaguar" CPU cores from AMD. Much ado has been made about the DDR3 vs GDDR5 issue, but I think its mostly a wash -- GDDR5 has higher bandwidth, but it also has higher latency -- game devs have gotten pretty good at optimizing their memory layout in a way that would favor bandwidth over latency, but its not always possible or practical, and it always contorts the classical Object-Oriented worldview that most programmers think in, especially those who aren't gamedevs or involved in HPC work. If your problem makes you jump around a lot in memory, or you just want to write your software in the classical OOP fashion (as opposed to DOD), then the XBox One is probably going to penalize you less than the PS4.
In general, the PS4 is clearly tuned for games first, while the XBox one is a more balanced approach that makes concessions in order to facilitate non-game apps and likely to bring costs down.
My prediction is that the PS4 is going to come in around $100 more expensive than XBox One, even with the new Kinect bundled in. Due to the nature of GDDR5 chips, and Sony's late change from 4 to 8 GB they've got to have a more complex motherboard (more chips (16 per console), more electrical signals), more manufacturing expense, and they're forced to use the largest capacity chips that anyone makes, and which aren't in common use on graphics cards. Combined with an even larger SOC than is in the Xbox One, Sony faces a very real threat of supply chain issues either due to yield difficulties with their SOC or with the GDDR5 supplier being able to meet their demand.
To make an over-used car analogy, the PS4 is like an F1 racecar, while the XBox One is more like a high performance sports car. The former is purpose-built to excel at exactly one thing, while the latter is something that's a daily driver and still no slouch at the racetrack.