Yes, it IS faster, but it's not SO much faster that it's worth the extra price to every person or for every situation. If your primary consideration is gaming, you probably won't actually notice an enormous difference between 2133mhz and 3200mhz on a modern Intel system unless you're benchmarking.
There ARE some minor gains to be had, no doubt, but if you took the exact same system and played any given game with the lower speed memory and then swapped it out for the fastest memory you could make run in that system, I really doubt that you could realistically tell the difference without running benchmarks that will pick up overall differences of a few seconds running the same tasks or games. It certainly isn't likely to increase your FPS or cause you to have greatly increased speeds when encoding or streaming video. Some, but not a lot. Still, faster is better if the price difference isn't a lot. Currently, it probably IS a lot.
Either of these kits would be totally fine for your system.
PCPartPicker part list /
Price breakdown by merchant
Memory: Kingston - HyperX Fury Black 8GB (2 x 4GB) DDR4-2133 Memory ($94.99 @ Amazon)
Total: $94.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-01-15 03:59 EST-0500
PCPartPicker part list /
Price breakdown by merchant
Memory: G.Skill - Flare X 16GB (2 x 8GB) DDR4-2400 Memory ($169.99 @ Amazon)
Total: $169.99
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2018-01-15 04:01 EST-0500