Like everything in life, it's a trade-off. I'll give you my evaluation, having used both:
The lower-end PCs (including netbooks and nettops) are generally not as rugged as the Thin Clients, which are built for continuous commercial use. PCs are usually configured to be generally useful systems, while the thin clients are very much "lean and mean" and tailored for a specific use. The thin clients typically have no fans and no moving parts and thus run completely silently.
OTOH, the full PCs will have FAR more storage (though it will be rotating storage, not flash) and are typically easier to configure (the thin clients are soooo stripped down, they can be more difficult to configure and diagnose).
Of course, the full PCs WILL need a great deal of tailoring and configuring. They'll be a ton of useless stuff installed that you'll need to remove and about a zillion services and things you'll want to shut off. You'll need to crank-down the firewall to make it as restrictive as possible.
On the full PC you don't have the advantage of the Enhanced Write Filter, so the system configuration is read/write all th time. This leaves the full PC more open to malware and attack than the typical thin client (which reboots and all disk changes are gone).
As I'm sure you realize, they've very different types of systems. Either will work as a streaming audio host. It just depends on which you prefer, and (probably just as importantly) which you can find for sale at the price you want to pay at the time you want to buy one. New, the HP 5710 (512MB/512MB) originally sold for over $800, and current thin clients (1GB/1GB) commonly sell today for over $600. Now, some of this is just greed because they're being sold to the less price-sensitive corporate market (where volume discounts are also rampant... they buy these things by the 100's, usually, not by the unit), but the cost to some extent also reflects the quality of the components.
I hope that sheds SOME light on the whole Thin Client versus Real PC thing,
Peter
K1PGV