Both devices receive the update simultaneously, though the update is not the same for both of them. Pixel phones have drawn the long straw in this contest, getting not only a number of security fixes, but also a a small list of improvements:

Improves “OK Google” and music detection (Pixel 2 and newer),
Fixes an issue for some devices getting stuck during boot (Pixel 3 and Pixel 3 XL),
Fixes an issue for some devices getting stuck in EDL mode with a blank screen (Pixel 3 and newer),
Improves Unicode Japanese language support (All Pixel smartphones),
Improves Titan M module (Pixel 3 and newer).

As for Essential, sorry, but all you get is some vulnerability fixes.