Choosing a cpu cooler

[Pendax]

So i'm building a DYI for my cousin, all the components have been selected and allmost bought, but i'm still in doubt about the CPU cooler. 
The build is: 

PCPartPicker part list: https://de.pcpartpicker.com/list/3L2nGG

CPU: Intel - Core i7-8700 3.2GHz 6-Core Processor  (€2289.00) 
Motherboard: Asus - ROG Strix H370-I Gaming Mini ITX LGA1151 Motherboard  (€1131.00) 
Memory: G.Skill - Ripjaws V Series 16GB (2 x 8GB) DDR4-3200 Memory  (€1336.00) 
Storage: Seagate - Barracuda 2TB 3.5" 7200RPM Internal Hard Drive  (€493.00) 
Video Card: Asus - GeForce GTX 1080 Ti 11GB Turbo Video Card  (€5699.00) 
Case: Thermaltake - Core V1 Mini ITX Desktop Case  (€355.00) 
Power Supply: EVGA - 500W 80+ Bronze Certified ATX Power Supply  (Purchased For €0.00) 
Operating System: Microsoft - Windows 10 Home OEM 64-bit  ($0.00) 
Case Fan: Noctua - NF-R8 redux-1800 PWM 31.4 CFM  80mm Fan  (€107.00) 
Case Fan: Noctua - NF-R8 redux-1800 PWM 31.4 CFM  80mm Fan  (€107.00) 
Total: €11517.00
Convert the Euro the Danish, those are the best prices i've been able to find. but what should i choose for CPU cooler.

i've considered both CRYORIG C7 and Noctua NH-U9S. the limitations being that the max height is 140 cause of the case. am i missing any real god tier coolers? and which would teoreticly provide the best cooling?

[WoodenMarker]

Out of the 2, the NH-U9S is easily better. You could get away with a cheaper PR Slim though: https://de.pcpartpicker.com/product/hyQRsY/be-quiet-pure-rock-slim-351-cfm-cpu-cooler-bk008