If I use Act of Treason on an equipped creature then sacrifice it while under my control, can I equip the equipment to one of my creatures during the same turn or does the equipment go back to the original owner the moment I sacrifice the creature?
You don't control the equipment.
Control of the equipment is separate to control of the creature. The same is true for attached auras, or any other kind of permanent. If something gives you control of one, you only control that one unless stated otherwise.
If timing allowed it (e.g. if you took control of the creature permanently, or with an instant-speed equip ability such as Cranial Plating), the equipment's controller could attach it to something else.
However, a lot of equipment cards give abilities to the creature. For example, Hankyu gives the equipped creature the ability to add or remove counters on the Hankyu. You could, for example, tap the creature to waste any counters they built up.
Conversely, Umezawa's Jitte's ability is on the equipment itself. The controlled creature's attacks would generate counters for the equipment, but the controller of the Jitte would be the one to activate its ability.
If you gained control of the equipment (e.g. Steal Artifact), it would remain attached to their creature, but you could use the equip ability to attach it to something else.
Anything attached to a permanent that you can control of does not change ownership of the equipped object. Equipment, Aura's, and Fortifications remain under their owner's control unless there is a control changing effect acting on them as well.
You'll notice that there are rulings on cards like Demonic Appetite, an enchantment that can only enchant a creature you control. It specifically address what happens if you're opponent gains control of the creature or of the enchantment, but not both.
Some sources from the Comprehensive Rules
301.5d An Equipment’s controller is separate from the equipped creature’s controller; the two need not be the same. Changing control of the creature doesn’t change control of the Equipment, and vice versa. Only the Equipment’s controller can activate its abilities. However, if the Equipment grants an ability to the equipped creature (with “gains” or “has”), the equipped creature’s controller is the only one who can activate that ability.
303.4e An Aura’s controller is separate from the enchanted object’s controller or the enchanted player; the two need not be the same. If an Aura enchants an object, changing control of the object doesn’t change control of the Aura, and vice versa. Only the Aura’s controller can activate its abilities. However, if the Aura grants an ability to the enchanted object (with “gains” or “has”), the enchanted object’s controller is the only one who can activate that ability.