Without knowing a lot of detail, I would say the mini. Reason being, unless you have a very high end synology model the processor in the mini would be faster which would enable better transcoding to your clients.
I can give you a few more definite options, if you want to provide some more details like;
- What model Synology NAS is it?
- What clients do you plan to watch your media on? (iPhone, Roku, on the Mac Mini etc)
- What sort of media fo you plan to watch (SD/720p/1080p/Full Bit Rate 1080p/etc)
Playing around I determined that my nas isn’t compatible so it isn’t an issue. It looks like my mini will stay as my plex server and will point to the nas for all the media. I have no issues with that.