I noticed this with my Nexus 5, and was surprised to see it continue with my new Nexus 6P:
I have a 5th generation Apple Airport Extreme. When I am using my Android phone on wifi, images load really slowly or not at all on apps like Facebook and the Google Play store. When I switch to LTE, they load right away. This is weird, because my speed tests indicate 100mpbs performance over wifi, and most other apps don't have any issue.