The fact that there is a measuring device in the box means that the device and its cat experience what they experience. One wavefunction experiences a poisoned cat, and one experiences a live cat. But outside the box, it has not been resolved which of these two wavefunctions will still exist once the box is opened. If you were the cat, you would not have two experiences: 'alive' and 'poisoned'. You would only experience one of them. It's just that there would be two cats having two experiences. It's kind of like peeling an onion.