Slow transfer speed over network

Normal of course it is not. I take it you mean a N3150 NUC, which should be more than capable of doing a proper network connection. But as you said, wifi is a totally different can of worms, Linux driver support can be flaky. Is there a chance that you can use ethernet on the NUC as well, just to double-check?

The onboard gigabit ethernet should be more than fine. Using wifi with any HTPC device should be banned in my opinion.

You need to remember that anything wifi is not equal. Your Beebox wifi antenna is hidden inside a box (metal or plastic), probably behind a TV and probably at a point as far from the router as possible. If you're using 5Ghz then the range is not as good as 2.4Ghz but speeds are greater.

For these reasons, I use 5Ghz with an external wifi adapter (with a large antenna) attached to an extension cable, so as to get the best reception possible.

iwconfig wlan0

That will show you the link quality and signal strength. If it's not around 40/70 and -60db then you're going to have issues for large files.

As a test, I placed my wifi adapter next to the router and got 70/70 -31db. Moving a metre away gave 67/70 -43db. Placing an anti-static bag over it gave 54/70 -56db. So even small things can affect the performance of wifi.