Lamapaseo:
Yes, both certified to fly with a single engine out. Both in need of a diversion with two engines out. And the one with more engines has a greater chance of independent failure combinations, not to mention the myriad of risks having nothing to do with muliple engines out.
No, the twin doesn't because it's going into the drink.
The four engine aircraft has a greater chance of an engine failure and thus a turn around fairly early in the flight. But, that chance is very small. Once you get far out the 4 engine aircraft is simply safer than the two engine aircraft, but the economics are not as good. So, ETOPS is all about money.
The greater chance of an engine failure "early on" in a 4-engine bird is an "insurance payment" for greater safety when out somewhere in the middle, more or less.