I've never heard that jet engines are less efficient. From what I remember piston engines are 33% thermally efficient, diesels 36% and turbine engines are upwards of 60%+. Of course there are many types of jet engines and ways to get power off of them.
You heard wrong. Diesels under optimum conditions can easily exceed 45%, and state of the art is right around 50%. Gasoline engines can reach 40% or better (again, under optimum conditions). Turboshafts are generally around 35-40% efficiency at best-economy conditions, and dismal under low-load conditions. The very largest turboshafts can reach 40-45%, but come nowhere near to diesel efficiency at low load.
In all cases, you can increase efficiency somewhat by going to the complication of compound cycle, where you harness some of the wasted heat in the exhaust by making steam.
Large, high bypass turbofan jet engines are very efficient from an overall propulsive efficiency standpoint, but you aren't measuring the same thing (shaft power times time, divided by energy consumption).
