When my pack of wolves killed a pillager captain for me, the pillager captain didn't drop an ominous bottle or a banner.
Attachments
Comments 2

Can confirm, affects 1.21.51. This is a parity issue, as they will drop both items on Java if killed by a tamed wolf. However, from my tests, they will drop the banner if they're killed by a wolf, just not the ominous potion.
Steps to reproduce:
Summon a wolf and tame it.
Summon a pillager captain using the following command:
/summon pillager ~ ~ ~ ~ ~ minecraft:spawn_as_illager_captain
Hit the pillager once so that the wolf attacks and kills it.
Repeat steps 2 and 3.
Observed results:
The pillager captain will drop the banner, but never drop the ominous potion. If the player kills the captain, it will drop the ominous bottle.
Expected results:
Both the banner and bottle should drop.