"I'm not following you re: price. The barebones model you listed is selling at a steep discount on Amazon but it's still $530, not including RAM and hard drive. The base model Mac Mini only costs $500 and that includes everything. So I'm not following your factor-of-two price difference comment."
That's an apples to oranges comparison.
The NUC5i7RYH model is the highest end model which should be compared to the 2.6/2.8GHz model configured with the optional i7 CPU, which brings the minimum price to $1000, and the processing power to about the same. The upgrade from 8GB to 16GB is $200, so it's $1200 for the Mac Mini - and this is only with the 5400rpm 1TB HDD model.
The lowest price for the NUC is actually $477.
The NUC fitted with 16GB (+ $100) for the barebone model is then 577. The same HDD type is about $50 so less than $650 altogether.
I selected the NUC5i7RYH model since you were talking about hw requirements 'not found on other computers of the same size' and compared it to the top Mac Mini model.
The base model Mac Mini should be compared to NUC with an i5 CPU, which would either be the NUC5I5RYK or NUC5I5RYH - the former an even thinner model. Those are $290 at Amazon.The 4GB DDR3L is about $30, so definitely less than $400 with the 5400rpm drive.
Obviously at the low end the price parity is nowhere 2:1, but if you're comparing a fully configured Mini to a similar NUC - it's close enough in my book.
BTW, drilling down to small details - the graphics in the NUC has support for 4K/60Hz whereas the Mini i7 "only" supports 4K@24Hz or UHD (3840 res)/60Hz. The OpenCL support in the NUC is also v2.0 vs 1.2 with the Mini. Therefore the NUC is a bit more future proof.