I've had them all!... a 1.4ghz i5/4gb/500gb HD 2014 Mini as a media server, replaced with a 2.8ghz i5/8gb 1tb Fusion Mini. I split the 128gb internal SSD from the hard disk and use it as the startup drive, with all my media on a 4tb external USB SSD. I also use this machine to stream audio/video with SiriusXM and Sling, watch iTunes video. etc. It's fine for that but I don't think I'd use it for Final Cut Pro.
Also had the base 2012 2.5ghz/4gb/500gb HD Mini and used it for a media server before I got the 2014 Mini. I would say that base 2012 Mini was a far better machine than the base 2014. I never saw the kind of "lag" on the 2012 where icons bounced endlessly in the dock before opening. And as a plus, RAM is easily upgraded to 16 gb on the 2012. I suppose an advantage of the 2014 is that it's easier to add a SSD than the 2012.
Now, I also have a 2012 top-spec Mini with the quad 2.6ghz i7/16gb/256gb original Apple SSD. That is much nicer than any of the 2014 Mini's. I used that machine pretty heavily for several years with Final Cut Pro, editing 1080p video and found it quite usable. It's now a file server for time machine and archival storage, but this is the primary use recently. These Mini's have always run warm, and the gentle purr of the fan is so soothing!