I've not investigated why Keccak is so much faster. Might have something to do with the compiler.
As far as "fraction of the price" goes:
7700K $300, motherboard $40 == $340 total
1800X $460, motherboard $65 == $525 total
7700K setup is 35% cheaper. Plus the operating costs are lower since it draws less power. Also don't forget that the 1800X lacks onboard graphics, so you'll have to buy a discrete GPU as well. We used a spare 290X that we had lying around. With the 7700K we used the onboard graphics, so no discrete GPU is needed. Plus you can use the onboard graphics for an additional boost in hashrate as well.
As far as "fraction of the price" goes:
7700K $300, motherboard $40 == $340 total
1800X $460, motherboard $65 == $525 total
7700K setup is 35% cheaper. Plus the operating costs are lower since it draws less power. Also don't forget that the 1800X lacks onboard graphics, so you'll have to buy a discrete GPU as well. We used a spare 290X that we had lying around. With the 7700K we used the onboard graphics, so no discrete GPU is needed. Plus you can use the onboard graphics for an additional boost in hashrate as well.