I'd go for a NAS (in fact I do have one)
The main disadvantage is possibly speed depending on your computer and home network, if you have a 1Gb network then the NAS is potentially faster than USB2, if you have a 100Mb home network then the NAS would be slower than USB2, if you use wireless then it would be far slower than USB2
I have my NAS connected to a 1Gb switch which my desktop is also connected to, my laptop uses wireless most the time, unless I want to copy large amounts of data to, or from, the NAS when I connect the laptop by Ethernet cable to get a 1Gb connection to the NAS.