Theft: Does a Returning Creature Keep Equipment?
Your instinct is correct, there is no difference between changing control due to stealing a creature with something like Wrangle, and changing control due to something like Wrangle's effect ending. The answer provided by the linked question remains exactly the same. In both cases, control of the creature is changing from one player to another; while control of the equipment stays with the player who originally cast and controlled the equipment.

The equipment will stay attached until something changes that. As the controller of the equipment, you could use the Equip ability to attach it to a different creature.