Simply from a stability standpoint, 1 engine gone on a 2-engine leaves one side rather unstable. Whereas on a 4-engine, ther is still 1 on that side to continue. Much more stable by nature.
The 2-engine is understandable from economy standpoint, but everything else being the same, it simply is mechanically unstable if just 1 goes out of 2.
The Boeing 787 and 777 are thus certified for up to ETOPS-330, meaning that they can fly for 330 minutes (five and a half hours) on a single engine. The Airbus A330 is certified for 180 minutes of ETOPS flying, and the A350 is pending certification for 420 minutes of ETOPS.