1. For an engines efficiency, look no further that its specific fuel consumption (SFC) and use the lb/(shp-h) as a comparison from one engine to another.
2. In principle, a reduction in SFC, means more range or better payload and of course reduced operating costs.
3. As for the most efficient engine type. It is going to be a recent design, incorporating the very latest technologies. Something like the GE38 on the 53K is around 0.4 lb/(shp⋅h), but I would hazard a guess that the GE T901 is even better and likely in the region of 0.3? lb/(shp⋅h).