Use the one that fits what you want to use it for. What does it matter which one is official or even if both are. Reskinning creatures is pretty common.
The Carrion Crown version was there first (2011), the Bestiary version came later (2015). It looks like the AP version was used as a starting point, but the Bestiary authors weren't content with it, so they beefed both creatures up and changed several details.
The Bestiary version could be seen as more official (as a replacement for the AP one). But I agree with Mysterious Stranger: Better pick what suits your campaign and everyone's fun best.
If you want to mix both versions and adapt the power level, I guess we can help.
I always assume things from an AP are written solely for use in the same AP. things like unique monsters, spells, etc., should stay in their source material IMHO
I'd view the AP version as a specific unique monster variant and the bestiary version as the standard
These monsters (CR 20 Grim Reaper and CR 10 Minor Reaper) appear in the backmatter bestiary of the AP, not as part of the adventure. All the APs include new monsters that aren't part of the adventure because there are bestiaries in all the books. So there are a lot of monsters published as backmatter in the books that aren't part of the adventures. They tend to have longer and more elaborate ecology entries than the hardback Bestiaries.
The creatures in the APs don't get as much development as the creatures that appear in the hardback Bestiaries, particularly if the Bestiary reprints the monster from an AP bestiary, so it's reasonable to think of the Bestiary version as replacing the AP version, at least stat-wise. In general, the AP bestiary entries still tend to have more ecology information on any given creature than the one-page hardback Bestiary entries. Sometimes they're in conflict though, as appears to be the case with the Grim Reaper entries.
The Lesser Death (CR 16) and Minor Reaper (CR 10) creatures look the same but are extremely different in their write-ups and power-level so I'd want both to exist. Also, minor reapers have a unique ability (sole target) where they can only target a single target, but if they're attacked by anyone else, they summon another minor reaper with their attacker as its sole target.
If I had to guess, I'd say the CR 10 minor reapers got upgraded to CR 16 lesser deaths because it makes them better suited to appear in an adventure with the CR 22 Grim Reaper without just being cannon fodder.
So anyway, my hot-take is that the Bestiary 5 version is the more official version since it's in the Core Rulebooks line and was published later, but just because a monster is from an AP's backmatter bestiary doesn't mean it's limited to that AP, especially since it may not appear in the AP's adventure at all. The stuff in the AP backmatter bestiaries tends to be on-theme with an AP but not necessarily part of that AP.
The Pathfinder cosmology is ultimately big enough for the Grim Reaper to have two different stat blocks though, and the GM gets to make the final decision.