well with a nas your going through your network so your speed is going to be limited to 100mb 1000mb or what ever speed your home network is running at.
Some advantages to a nas are that it is on your network like another computer almost and so any pc or laptop on your network can be set up to access the storage space on the nas. Also most nas can be set up in a RAID configuration so, depending on what raid you set up, you can get a back up or some performance out of the nas.
A downside to the nas would be the extra cost put into it, both in more than one hdd (if you want to raid), and the "case" that holds the hdd's are usually not on an extremely cheap side.
with an external hdd you are hooked up directly to the pc via usb or external sata, firewire, ect. Also you can set up any hdd in a pc to be shared on your home network (if you need that). And the real good thing is you can get an external enclosure very cheap now.
So for you I would recommend an external enclosure because its the cheapest way to add storage space (well except for just adding a hdd into the pc but you cant do that
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