FWIW my opinion is, the Coyote is probably the most advanced of the three. Hard to beat multiple cams and the advantages that cam phasing adds to that, on top of 4 valves per cylinder (funny, it's about the heads again). Heck, as I understand it, Ford even engineered the oil system for horsepower. At the same time, the physical size of the motor is a real detractor, and the high rpm nature plus the lack of cubic inches makes it feel a little "mundane" around town (at least in my experience while riding in a buddy's '13 GT). Just didn't seem like it had much low end torque. My brother just got done building a trick '55 Vicki with a crate Coyote for a guy and will be taking to all kinds of shows this summer, and he doesn't drive anything softly, so I should have another comparison by the end of the summer.
I think the 3G Hemi heads give that motor a technical advantage over the LS, but it loses out on the size.
Only advantage the LS has (if you ignore costs) is it is smaller and easier to fit. If I were to move over to an E36 BMW, I would probably look really hard at putting an LS motor in it.