I've had three shutdowns on four-engine airplanes.
1. KONT-PHNL: Turbine failure, shutdown, dump, return to departure airport.
2. PANC-RJAA: Slow loss of oil, have lunch and monitor, low oil pressure light confirmed by OP gauge, shutdown and continue 1.5 hrs to destination. Pinhole leak in oil line.
3. RCTP-RJAA: Loss of oil pressure after takeoff by 10,000', shutdown, continue to destination. Oil tank cap missing.
If flying a two-engine airplane, situation one would be no change, situation two would have been a diversion to an Aleutian chain airport and situation three would have been an immediate landing back at departure airport.
A four-engine airplane gives you more options, including continuing to destination for all the obvious reasons. The other thing to consider with a two-engine airplane besides ETOPS requirements is terrain enroute should an engine fail. Our two-holers had to fly different, more lengthy routes on some sectors than our four-engine airplanes.
I know I'm prejudiced, but I would much rather operate a four-engine airplane (and have since 1977) for the reasons outlined.
Edit: One also has the option of a three-engine ferry to a more capable maintenance base, which is not an option with a two-engine airplane.