Well you can't really compare a projected image with a flatscreen image - they're different beasts. Projectors, even those costing 10x more that yours or mine, are still only SDR display devices - they can never reach the nits levels required for true HDR which I would say is a minimum of 1000 nits (most projectors struggle to get to 100 or so). So something has to tone map to SDR, whether it's the projector itself by receiving an HDR signal or the source as in your case. The Zidoo does a great job of it (the newer models are slightly better!) so a better test is to compare the HDR results of the projector vs the SDR results of the projector.