A Vortexbox is a computer running free Vortexbox software - almost any computer with PC architecture can run Vortexbox software. You can DIY or get one pre-built from Vortexbox.
Once installed, the computer becomes a Vortexbox appliance. It is no longer a multi-purpose computer like a Mac or PC.
Depending on which hardware you choose it can
rip CDs with CD Paranoia
serve music files to a Naim, Linn, Cyrus, Sonos, Logitech and other players
serve files to a PC or Mac Mini
play out of its USB port to a DAC
play through a sound card over S/PDIF to a DAC
you can store files on it whether you have ripped or downloaded them
it supports any format when it serves files
it plays FLAC directly if you use a sound card or its usb port
you can tag things or get it to do that for you
same goes for cover art
it just works - not much messing about if you buy it pre-configured for your needs
it supports almost as many discs as you like either in RAID (for making two copies) or without for lots of space (20,000 CDs).
you can back it up by attaching a suitable disk to its usb port
it makes the tea
it is very versatile
support is what you would expect for a free software product - forum folk do their best to answer your questions, but you could be left on your own if you get stuck
The US on the other hand is made by Naim and works in a way that Naim thinks is best for its products, so it is more restrictive. However, it comes with Naim build quality and service. If you buy the SSD version you still need a NAS for your music. If you buy the HD version you can store files you have ripped, but not ones you downloaded - for this you need a NAS or to use USB sticks. The US works as player or music server and you can use the nServe app to drive it. You do need a PC to edit things as there is no Desktop Client for non-Windows systems nor is there an agnostic method using a web browser to edit things (e.g. to change the cover art).
Naim sells through dealers who help you install it, Vortexbox is sold on-line.
I prefer the Vortexbox approach, but I can easily understand why other prefer the US. They both work and ultimately neither is better than other.
One parochial thing is that Vortexbox uses absolutely nothing from Microsoft so not one brass farthing goes to them, but that makes very little difference to the way it works. It just satisfies those of us who are of a pomaceous persuasion.