I've got the older Fire TV stick (without voice control) and the interface is a little slow. Also if using some apps (like iPlayer) the audio gets out of sync with the picture, so I end up putting the audio through my surround sound enabling me to delay the audio and get it back in sync. This problem doesn't occur when watching Prime content through the native Amazon app though.
Not tried using Netflix through the Firestick though.
We did have Netflix previously but watched it through an Apple TV, which had no problems in playback and had the benefit of a box with connections for a network cable (ie you don't need to use WiFi) and digital audio out.
Both Netflix and Amazon Prime have similarly-sized selections of movies, but not the exact same movies. Prime does get frustrating when the movie you want to watch is displayed but NOT available unless you pay extra to rent it.
Prime does have the advantage of being able to swap between your mobile and the TV stick. You can even search the database on your phone (often easier if you are using text search) and then send the movie to the TV. There's also a remote control app if you misplace the remote.
The Fire TV is nice and portable though if do want to have the option of taking it away with you.
If you are getting rid of a Sky/Virgin package, I'd consider getting a Freeview Play box. This'll get you all the TV recording you want plus iPlayer and other on demand apps and many have a Netflix app too. Try looking at
Humax