Xbox One isn't the only next-gen console unable to play 3D Blu-rays, with the official PS4 manual listing "Blu-ray 3D" under unsupported media.
The manual states that supported disc formats are:
- BD-R/RE (BDAV, BDMV)
- DVD-R/RW (video mode, VR mode)
Playback of the following types of discs is not supported
- BD-RE ver.1.0
- BD-R/RE XL
- Blu-ray 3D
- DVDs that have not been finalized
Microsoft has said it hasn't "ruled out adding the feature in the future" whilst Sony is yet to comment.
Given that Sony offers many standalone Blu-ray players which support 3D movies, and that PS4 is 3D-gaming capable it seems bizarre that PS4 doesn't support the format.
Source: PS4 Manual