Why is a Xbox One S much cheaper than PS4 Pro?

The PS4 pro has much higher specs than the Xbox one S.

Xbox one S is like new slim version of the PS4.
Xbox Scorpio coming later this year, will compete with PS4 Pro

Specs don't matter! (*cough*iphones*cough*). It's all about popularity. In Lebanon nearly maybe 75% of the people own a current gen ps4/ps4pro while xbox1/xbox1s are few people!
The opposite situation to the xbox360 and ps3 situation in the past.

Xbox One S is slimmer version of the Xbox One with a minor OC of the GPU /CPU the major upgrade is a 4K BlueRay Drive that is HDR Compatible. The PRO outputs a 2160p signal which the Xbox S out puts this signal for streaming / 4K Blue Ray and games are upscaled from 1080p to 2160p. Some Games on the Pro (Few like Fifa 17 runs native 4k/60fps on the pro) Other run native 1440p/60fps like Battle Field One , Titan Fall 2 .. and upsacled to 4k, and also some titles uses 1800p checker board technique which has a base reolution of 1080 × 2160p on all cases the image fidelity is much better than native 1080p upsacled to 4k. Some Games also push 30fps to 60fps on 1080p on some Pro patched games (perfomance mode usually like Rise of the Tomb Raider).

In Short in raw gpu computational power:

PS4 ~ 1.84 TFLOP
PS4 Pro ~ 4.2 TFLOP
Xbox One ~ 1.3 TFLOP
Xbox One S ~ 1.4 TFLOP

Note: Xbox One & One S Uses DDR3 while the PS4 / PS4 Pro uses DDR 5 for the OS and GPU ( The Pro Added an Additional 1GB ~ 9GB of GDDR5 )

Xbox Scorpio is expected to have 6 TFLOP ( GTX 1070 ~ 6.5 TFLOP as an example)