Microsoft confirmed to CNET that 3D Blu-ray isn't supported right now, but didn't rule out adding the functionality at a later date. The PlayStation 4 (PS4) does support playback of 3D Blu-ray discs.
Still, the demand for 3D at home hasn't been overwhelming by any means. In the long run, support for 4K video output for example might be a more interesting development. HDMI 1.4 supports 4K2K (though at 30fps), so it's likely that both consoles will support video in 4K before long as more 4K TVs roll-out onto the market over the coming years, while the consoles age and update to stay relevant.
According to Sony, the PS4 does not currently support 4K but it has said in the past that the hardware is there, and it technically is (for video playback rather than gaming). Microsoft's 'Major Nelson' made a statement that every Xbox One console ships with a "4K HDMI cable", but that's a worthless statement given that all high-speed HDMI 1.4 complaint cables are technically 4K-ready. It doesn't tell you anything about playing 4K video with the Xbox One.
Do you care about 3D or 4K video playback on either console?