Suppose you have cards attached to a creature, and then use Creature Swap. Do those attached cards follow the monster to the other side of the field?
So I know my comment started this question, and if you want someone else to answer I understand. But here is why I do not think they go with the creature. The official rules about equip cards:
These cards give an extra effect to 1 face-up monster of your choice (either your own or your opponent’s, depending on the card). They remain on the field after they are activated. The Equip Spell Card affects only 1 monster (called the equipped monster), but still occupies one of your Spell & Trap Card Zones. If possible, place it in the zone directly behind the equipped monster to help you remember. If the equipped monster is destroyed, flipped facedown, or removed from the field, its Equip Cards are destroyed
So it points out that Equip cards you control can in fact be on monsters your opponent controls. Creature Swap only says it gives your opponent control of the creature. Not anything else. In my mind the objects attached to the creature would still be under your control.