In terms of performance characteristics, what are the tradeoffs between a 2-engine and 3-engine design?

Lets assume that we are comparing a twinjet with fuselage mounted engines and a trijet with an s-duct layout and all engines on the fuselage. I think its unfair to compare to a trijet that would have 2 wing-mounted engines. It seems structurally inefficient on its face.

I read all over the internet that 2 engines is always more efficient than 3. But is that necessarily true?

It seems that a main factor is the requirement that a plane be able to complete its takeoff run with one engine out. On a twinjet you're losing 50% of your power while on a trijet you are losing 33% of your power.

So take two hypothetical airplanes and hold pretty much everything equal except the number of engines at the back. If the plane requires 0.5X thrust to complete takeoff, then the twinjet needs total of 1X thrust while the trijet needs 0.75X thrust to takeoff with the same runway requirement.

At cruise, which plane is more efficient? The one that is uses the three smaller less efficient engines or the one whose 2 larger engines that are incredibly overpowered for cruise? By how much?