If I play hostile takeover and attach equipment to that unit, does the opponent get my equipment when I lose control over the unit?

No — the opponent never gains control of your equipment. When a unit changes controllers, attached equipment stays attached but remains under its original controller's control, so the gear is still yours when Hostile Takeover's end-of-turn effect gives the unit back.

The equipment just rides along with the unit to the opponent's base and keeps working while attached. It only comes back to you if the unit leaves the board or the equipment detaches — at which point it's Recalled to your base (Rule 457.1). One quirk: while it sits attached at the opponent's base, it's a gear you control in another player's base (Rule 106.2.d territory), which is a known rules gap rather than a control transfer — nothing about that hands the gear to your opponent.