The aerodynamics guys (and gals) will tell you a tail fairing adds more speed than a front fairing. I installed a Streamer fairing onto my Trice QNT quite a number of years ago and although it has helped a bit with speed (a bit more than I was led to expect!), a big advantage is when you’re riding into headwinds – it definitely reduces the effect that they have, to the point that there have been occasions in very strong wind. where I have passed roadies going in the same direction as me. That’s not something that happens very often otherwise. The thing to bear in mind is that they tend to only have an effect over 16mph in still air, but ride into a 30mph headwind and you’re in the benefit zone no matter how slow your actual road speed is.
They’re also good at keeping your legs warm in winter and keeping the rain off. And with the wind in the right direction you get a sail effect. I’ve never found it difficult in crosswinds, perhaps because I’m low down. I’m sure some of these things will apply to tail fairings too, but for me the Streamer is lighter and more practical for my uses.
I think the picture you linked to shows a fairing that’s mounted a bit too high to be optimally useful: I contrived to get mine mounted so it was as low as possible at the front and just cleared my knees at the rear. Short cranks (145mm in my case) help a lot in this. This ensures that the majority of first contact with the wind is with the nice smooth fairing and not knobbly trike or body parts.
Of course it depends on the ergonomics of your trike. I haven’t tried it but I don’t think the Streamer fairing would work on my VTX because I’m much more reclined, and I suspect the same is true for the Catrike 700.
I bought my fairing thinking I’d be taking it off in the summer, but it’s actually only been ridden twice without the fairing in about 10 years, and it went straight back on each time. Even on the turbo trainer
(though it does tend to steam up a bit!)
Welcome to the treadmill 
