I believe the reference book on the topic is "High Altitude Medicine and Physiology " by Ward, Milledge, and West. I have the 3rd Edition (2000) sitting in front of me.
They say:
The barometric pressure at the Earth's surface and at 24 km is essentially independent of latitude. However, in the range of about 6-16 km, there is a pronounced bulge in the barometric pressure near the equator in winter and summer.
Therefore, Everest at 6 km has more oxygen than Denali at 6 km. They say the cause is a very large mass of very cold air in the stratosphere above the equator.