Unsurprisingly, Microsoft has announced that Xbox One is DLNA-compatible. Sony recently revealed that PS4 will be lacking many media capabilities at launch, including support for MP3 and audio CD playback. Being the "all in one entertainment" box, Xbox One does support these formats, albeit with a few caveats.
MP3 playback is not natively supported out of the box either, according to The PA Report. However, you will be able to stream music from a Play To device running Windows 7, 8, or Windows Phone. You can also run Xbox Music Pass, a similar service to Sony's Music Unlimited.
You'll also be able to listen to music from audio CDs, something PS4 doesn't support either for some reason.