Speaking for the 777
mins at heathrow for instance
takeoff 777-200 (cat c ) vis 125 m
landing Cat IIIb vis required 125 m DH 0
777-300 (cat d) vis 150 m
also 150 for Cat III b landing
1 or 2 engine makes no difference
vis segment for both is 90 m required. ie must be able to see, from the flight deck an unlit object, the size of a person at 90 m from the nose of the aircraft
However, these are reported v is from the RVR sensors.
What is defined as visual ref at min for a III b is any single light, sufficent to judge the lateral placment of the aircraft. There is no time to make an assessment of ability to keep the aircraft staight, just that it will be on the runway. Some of the vis requirement also to do with being able to get the aircraft off the runway safely. Ground radar is fine, but it can't turn the thing.
These are company mins, buteach operator has to be approved by the dept of the country in which the appr is taking place.