That wouldn't account for such a large difference.
It is possible your NAS has security/malware software that's inspecting each network packet? You often see this type of problem when your PC is using McAfee, Norton, etc. These can dramatically slow down your transfers. Of course, that's coming TO your PC. You have the problem in the opposite direction. But since I don't know anything about your NAS, it might still be possible (e.g., Windows Home Server).
If you’re not sure, I would test w/ a wired connection. If you get the same asymmetric results, it probably is something like anti-malware getting in the way.
Btw, is the NAS also using wireless? If so, what speeds does it get between itself and the wireless router?
Well it may be the NAS to blame then, maybe it can't write as fast as you think it can/should! That's why I said, test w/ a wired client too. If the wired client is no better, then you know it's NOT wireless to blame, but more probably a limitation of the NAS.