First watch is a total frankenjob, IMHO. Never seen Grand Luxe dial like that on 55X series movement, and 168.XXX case reference means that there should be a date feature. No exceptions.
Second one looks correct, but not in good condition. One would think that on an otherwise $4K watch, you'd invest $200 or so into a good clean-up of the movement and a proper crown.
Not sure what to make of these listings,
gatorcpa