They didn't drop much on their main markets (USA and UK), in fact they tracked ahead on those for about 3 years, so how would you explain almost zero impact on their main markets with they dropping dead everywhere else? Did only people outside of USA and UK watch the presentation?
They took several years to be able to put the price on market acceptance while never being cheaper than X360. X1 solved most of the issues even before release (always online, DRM, TV, etc), had more exclusives at launch and before even 1 year in the market always sold cheaper than PS4.
The market for consoles is constantly growing and you seem to have forgotten about the WiiU. With WiiU being a total flop there were only two major players in the consoles market during the start of PS4/X1 generation.
Sony built well deserve brand recognition from their PS1 and PS2 era and once the PS3 reach price parity with the 360, they clawed their way back to eventually won that generation.
Mostly because their dominance in the Asian market and they have a very strong foothold in Europe/USA/World. They been the market leader for last three generation (Yes, I'm ignoring the Wii since that console mainly capture a fickle casual market that bought the console mostly for Wii Sport). Only reason Microsoft even had a moment to shine with 360 was because of PS3 awful price point at launch. PS3 was always slightly more powerful and feature a blu-ray players which explain why the console was always more expensive.
X1 never solve the main issue until they release the Xbox one S(slightly less powerful but offers feature that make it on par with PS4), there consoles was less powerful and they tried to sell it at higher price since it included a peripheral that no one wanted. X1 also never won the exclusives at launch because they ignored indies. There is no way X1 can recover in market they were never strong trying to sell an inferior product compare to Sony. Phil Spencer and his team has done an amazing job putting out all the fires and really offering value to their customers that Sony can't match or doesn't care to match. Xbox Play anywhere, Xbox game pass, backward compatibility & EA Access.
Tommy Jean, CPA, CGA