Fuel burn at idle is very small, whether a diesel or gasoline engine is involved.
With both, the throttle plate is almost fully closed, allowing only a very minimal amount of air to enter, and in both, the pulsewidth of the injector spray will be minimized to maintain a proper ratio with the volume of air being allowed to enter. It takes little energy to turn over a warm engine that's not connected to a drivetrain. The major loads are really just the alternator and (if you have the AC on), the AC compressor. Unless you're turning, the PS pump is free flowing, circulating the fluid, so it adds little in the way of load.
As a matter of fact, there's so little power being applied by the cylinder that the idle has to be "bumped up" a bit to run the AC compressor should you turn it on.
A hybrid setup uses less fuel by shutting the engine down when you stop until the battery drops a bit and starts the engine again, because although ultimately the energy used from the battery by any accessories that happen to be on will need to be replenished by the gas engine, at least little of the electrical power is converted to heat as opposed to the amount of energy that would go out the tailpipe if the gas engine were running. But I'd argue that the differences are minimal, although they're enough for the industry to be using this approach in their quest for maximum efficieny and minimum emissions.
I've never been a diesel fan. Diesels by their very nature have to run at higher temperatures and compression ratios, and that creates more NOx. While I'm of the underatanding that the new systems can scub that out, scrubbing a bad emission out is not as good to me as not creating it to begin with. There are always tradoffs. I also wonder how well these systems will work when they get old.