Just to let you know, I have successfully set up a working OSMC Raspberry Pi Zero configuration.
Whilst the install and menu operations are noticeably slower than the RPI2, the video playback and streaming is just as good EXCEPT there is a noticeable difference when playing ISO files (and I guess the same would be true for playing direct from a DVD).
NB This is not my main OSMC setup - I am still using the RPI2 for normal day-to-day use.
Do you have the decoder licences? Otherwise it is quite clear that MPEG2 playback on the Zero will be terrible.
@StartledCat - if you have not heard of the decoder license before, look here for info: http://www.raspberrypi.com/mpeg-2-license-key/
The license costs a few dollars and enables hardware decoding in the Pi:
This key will enable a single Raspberry Pi to decode MPEG-2 video in hardware. You will need to provide your device's internal 16-digit serial number as part of your order. Your serial number is not the number printed on your board.