I found the problem files. It was 20GB worth of stuff copied from a USB stick, files from a friend. I deleted the lot and the "deleted items" copy and now I can enable Content Sharing without the box crashing.
The funny thing is, my other HDR Fox T2 has exactly the same set of files on it and that one isn't crashing. So either the two boxes are behaving differently despite running the same software versions, or at least one of them had an error reading the files and they each ended up with slightly different versions.
Thanks everyone for your help.