The Squeezebox approach is a client / server based distributed architecture.
If words like that make no sense to you, start with something like
Beginners Guide - SqueezeboxWiki
Once you understand the concepts, you'll see that the Squeezebox is a "thin client" - you'll need a computer somewhere ( or use one of their servers "in the cloud" at Home - Welcome to mysqueezebox.com! ) running their server software.
Then to confuse things, just when you though you had it all figured out, The Touch actually contains an embedded computer, capable of running a slimmed down server, capable of reading music files from an attached USB drive. The hardware has been ready for some time. It's the development of the associated software that has been holding up the release.
Both the SB3 and the touch have S/PDif Coaxial and Toslink Optical digital outputs suitable for connecting to the DAC in your 840C.
I leave it to you as to where you stand on the audibility of different digital inputs (and their implementation)
Given that the server sofware is free for download, and there are a couple of software client emulators around, you don't need to actually buy anything to play around with the system to see if it fits your needs / uses.
Looking forward, it seems likely that the touch is a more capable platform than the SB3 (and it can output 96/24 unlike the SB3 (which would have it downsampled to 48/24 on a server) )
Ultimately, it depends what your requirements are. Only you can answer that question.