OK, I HAVE run BI on a few Intel NUC's, from a celeron, YEAH !! for testing, but mainly 2 x i7 5th and 7th gen machines.
I had the machines and decided to test with them, I have the full height units units, so I have 2 drives (SSD), I used Windows 10 professional for the OS.
Operation is acceptable, they both have 16gb of memory and pretty fast drives, I also pass storage to a mapped NAS when needed.
BUT and this is the issue as 'I' see it, the CPU is an i7, but think of it as a cut down version, or maybe a laptop variant if you need to, it is NOT the full meat eating i7 in any way shape or form, and as such you will without doubt...
Hear the FAN spinning up and down a LOT, I repeat A LOT, so the initial remit of the quiet, cool and power saving functions will be pissed out the window very quickly.
And before the shitstorm start, I strip the units down, thoroughly clean and prepare the CPU with new high quality thermal paste, I also check and replace if needed the 'gum' tabs on the VRM/Memory chips, I clean and lubricate the fan unit and make sure the BIOS settings are optimized for noise/performance, I test each setting in the BIOS to see if it will reduce the spinning up and down on the fan, NADA, it appears to me on the units I have to make no difference.
As an aside, I also have an old Dell 9020 i3 SFF unit that I ended up using instead, it stays cooler, WAY more silent and just works, THAT is what people are eluding to when 'pushing' you towards the SFF and not the NUC devices.
As I have said, I have done some extensive testing on at least 3 NUC devices as well as a SFF unit, my aim was for a quiet unit, I have no issues with power consumption, but I do not want to have some big ugly PC sat around, and my honest opinion is that a NUC is not a long term solution.
You also mentioned running additional process driven apps as WELL as BI, this will only make things worse, too may times people want to drop the likes of PLEX server on as well, thinking the machine is sat around doing little, and yup did that too during testing, and some people will get away with doing all these things and say that they never see any performance issues, my testing showed otherwise, and as always YMMV as YOUR expectations may/will be different to mine, you (or your dad) may well be happy with the outcome, the unit may be out of hearing/sight and not be of concern and the performance acceptable.
To answer the original ?, Both will work, but not without compromises.