For $664.26
http://pcpartpicker.com/p/49cd8d you can buy an ITX motherboard, CPU, case, PSU and even a GPU. Needs memory and storage added, same as the NUC, after all it's the same price.
How much faster wil this be? Intel's own benchmarks show Iris Pro 580 to be between a 750 and a 750 Ti. The GTX 960 is about twice as fast as a 750 Ti. http://gpu.userbenchmark.com/Compare/Nvidia-GTX-960-vs-Nvidi...
CPU wise the difference is much smaller, I couldn't find a direct comparison but I found for the 6700HQ but that's just as good because the 6700HQ and the 6770HQ uses the same CPU http://ark.intel.com/compare/88967,93341 and then user benchmarks show the 6700 desktop a 20% performance benefit over the 6700HQ http://cpu.userbenchmark.com/Compare/Intel-Core-i7-6700-vs-I...
Of course because you are not restricted by the integrated parts if you were to spend another $150 then you can get a GTX 970 which is thrice as fast as a 750 Ti and in three weeks when the GTX 1070 lands at the same price as the GTX 970 that'll be four-five times as fast as the GPU in NUC.
For the NUC to be competitive, it would need to be $499 perhaps $549 and the external GPU box $150 tops. Now that'd be a very different ballgame -- at that point we would need to look at the significant size advantage and concede that the much smaller ITX cases are typically small run and tend to be more expensive so then the NUC+GPU box would give them a run for their money when space is at the absolute premium. At the current $699 and $499 prices it's hard to see their niche.
Here's an example for a real small, artisanal :) ITX case for when space is at an absolute premium: http://nfc-systems.com/shop/s4-mini-chassis You could buy this chassis, the necessary accessories as listed on the page, a GTX 960 GPU ITX card for the price of the NUC + Razer Core and end up with a single box barely bigger than the Razer Core still packing a much bigger punch. Here's a forum post http://www.superbestaudiofriends.org/index.php?threads/post-... mentioning a similar build (i5 6600 vs i7 6700 is the only diff, it might worth the savings actually).