As I mentioned, it entirely depends what you're trying to achieve -- and at what resolution.
Editing/Rendering/Programming may well benefit from the added cores/threads. Depending on specific applications though, there's an equal chance the higher clock speed could be more beneficial.
From a gaming perspective, at 1080p yes; there would likely be substantial performance gains with the i7.
BUT
If you're gaming at 1440p or 4K (which I'd hope you are with a 1080TI) then you actually see very similar performance on average (although there will be some variance title by title, of course).
As you'll see here:
https://www.techspot.com/review/1505-intel-core-8th-gen-vs-amd-ryzen/page6.html
Even at 1440p, the gap is within ~5% generally (paired with a Vega 64) between the $225 Ryzen5 1600X (and likely the 1600 too) and the $380 i7-8700K. 95% of the performance at stock speeds, for 60% of the cost. When you step up to 4K benchmarks, the gap is pretty much non-existent.
So, from a gaming perspective.... it's not going to matter much at all (outside of a few specific titles)
So then it really boils down to how heavily you want to build around your other goals; editing, programming, VMs etc.
Realistically, performance-wise (in Gaming); the difference between something like this:
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD - Ryzen 5 1600 3.2GHz 6-Core Processor (£159.54 @ Aria PC)
Motherboard: MSI - B350M PRO-VDH Micro ATX AM4 Motherboard (£64.97 @ Amazon UK)
Memory: Corsair - Vengeance LPX 16GB (2 x 8GB) DDR4-3200 Memory (£142.98 @ Ebuyer)
Storage: Crucial - MX300 275GB M.2-2280 Solid State Drive (£67.39 @ Amazon UK)
Storage: Seagate - Barracuda 2TB 3.5" 7200RPM Internal Hard Drive (£55.00 @ Aria PC)
Video Card: Zotac - GeForce GTX 1080 Ti 11GB AMP Edition Video Card (£685.00 @ Aria PC)
Case: Cooler Master - MasterBox Lite 3.1 TG MicroATX Mid Tower Case (£39.67 @ Scan.co.uk)
Power Supply: SeaSonic - FOCUS Plus Gold 550W 80+ Gold Certified Fully-Modular ATX Power Supply (£74.99 @ Overclockers.co.uk)
Total: £1289.54
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-01-02 21:42 GMT+0000
And the build you proposed would be negligible at best. While saving you 860 quid.