Nexus 6P charges slowly on stock 6P charger, but 5X charges rapidly
Background Information


From Nexus


  The Nexus 5X and Nexus 6P use USB Type-C for charging, so not all cables and chargers will work with these phones. We recommend using the charger that came with your Nexus.

Also corroborated here for LG Nexus 5X
Decent comparison of  Type C Charging. Point to note is that current supplied can go upto 3A unlike conventional charging or Qualcomm Quick Charge 2.0
When your device gets 3A it displays "charging rapidly" and when it gets 2.1A (conventional charging),  it displays "charging". This can be verifed by using an app like  Ampere


Analysis of symptoms described by you


To start with Nexus 6P/ Nexus 5x in any charger/cord combination
gave "charging rapidly"
6P Charger + 6P Cable on 6P &rarr; "charging"
6P Charger + 6p Cable on 5X &rarr; "charging rapidly"
5X Charger + 6P/5X Cable on 6P &rarr; "charging rapidly"


Conclusion from above &rarr; 6P Charger suspect


Later, 6P Charger + 5X/6P cable on 6P  &rarr; "charging". 
By this statement , I guess you mean 5X/6P Charger and 5x cable on 5X   &rarr; "rapidly charging"



  So now my Huawei phone can't charge at full speed with the Huawei charger, but my wife's LG Nexus 5X can without issue


Conclusion from above &rarr; 6P Cable suspect   

You could purchase a 6P Cable from here, being Google recommended and it should be fine IMO and verify current using Amplify app. If that doesn't fully fix the issue, then you may need to purchase 6P charger also as indicated from 6 to 8

I don't think it is OS issue since switching to stock didn't help (your question doesn't make it clear if custom OS was flashed only on 6P or both)- only way to rule this out entirely is by switching to stock on both

Let us know the result

EDIT:  Based on the clarification by OP , I strongly believe that replacing 6P  charger should fix the issue (since cable issue is ruled out) and nothing points to device problem All the best