Documents
Both passports, with their expiry dates
The document vault holds every passport and warns you before one runs out.
Entry rules attach to the passport you show. One of yours may be waved through for months where the other needs a visa. Residency keeps both and uses the one with the longer stay when it plans a trip.
Use one passport for the whole visit to a country, and check whether either of your countries expects you to enter on its own passport.
Documents
The document vault holds every passport and warns you before one runs out.
The one that gives the longer visa-free stay at your destination, used for both entry and exit. The comparison above shows which that is.