Do artifacts equipped on a creature transfer with Mind Control?

The equipment remains under the original player's control. It is not unattached, so Butcher's Cleaver would still have its effect on the creature, but the original player would be able to equip it to another as per the rules for equipping.

The equipment stays attached, but control of it does not change. This (along with Enchantments like Pacifism) is one of the rare situations where something one player controls can end up on the part of the battlefield in front of another player. In most cases, the equipment's effect on the creature stays in full and who controls it has no impact on that aspect of it. However, the controller of the equipment can then just re-pay the Equip cost and equip it to another creature they control on their next turn.

The Equipment remains attached to the creature, however control of it doesn't change. That means that the creature still gets the bonuses from the Equipment, but the Equipment's controller can use the Equip ability to move it onto another one of their creatures.

As a side note, one thing to keep in mind when you're confused about a card is don't make stuff up. Cards tend to do exactly what they say they do. 95% of questions that take the form of "Does card X do thing Y?" can be answered with "Does card X SAY it does thing Y?". Since Mind Control says nothing about the Equipment going with the creature, you can safely assume it doesn't affect the Equipment in any way.