Does one get Better sound from a network bridge + NAS or a Music Server w/ a Drive for Music?

A properly implemented Ethernet solution allows for better sound than any "server" in the audio system. As with anything in audio, the implementation is critical. The advantage is one can get all the commercial grade computer components (read noisy and built to the most affordable price points possible) away from the audio system. Put your "server" or NAS in another room in the house, along with the router, and power it from (hopefully) the other phase of your AC power from the audio system. Then use the best Ethernet endpoint you can get. The advantage is you now just have a low power Ethernet endpoint, designed and built specifically for high end audio use, with (hopefully) perfectly implemented low noise power supplies, and a very low power processor and dedicated custom designed OS, in the audio system. The result is less noise and RFI which can, and will, couple into the DAC clocking and analog side of things, reducing detail retrieval and often hardening tone.