It's all theory. The measure is how well it predicts. If you're looking for a concrete epistemology of what a photon is, you will not find it.
The way I think about your photon is the many-worlds interpretation, where instead of each "world" having a probability, it has a probability amplitude, which is a complex number.
If a world had only a probability, and you didn't know which world you were in, but knew you were in some set of possible worlds, then you would get the probability of that set by just adding the individual probabilities.
However, since worlds don't have probabilities, but amplitudes (which are square roots of probabilities), then to find the amplitude of a set of possible worlds, you add their amplitudes, and since those are complex numbers, they can reinforce, or cancel.
So you don't know if the world you are in has the photon going through slit A, or slit B, and landing at location C.
But if you add the amplitudes of those two possibilities, you get a combined amplitude, when squared, that can be more, or less, than simply adding the probabilities.
So the question isn't, which slit did the photon come through, but what's the amplitude, and therefore the probability, of the set of possible worlds we are in.
It's just a mathematical model, but it's the one that nature seems to follow.
If two atoms differ only by the spin of their nuclei, then their individual properties will be almost identical, but their collective properties will be extremely different.
Chemists often consider individual atoms (or, more often, molecules). In the case of individual hydrogen and deuterium atoms, their electronic properties are identical (except for the hyperfine spitting of their electronic energy levels due to spin-spin coupling between the electrons and the nuclei). Practically speaking, the only important difference is the mass difference due to the extra neutron.
But once you put a bunch of them together and lower the temperature enough that quantum effects (specifically multiple-occupancy of energy levels) become significant, their extremely different many-body properties become manifest. For example, neutral hydrogen atoms are bosons and can in principle Bose-Einstein condense, while neutral deuterium atoms are fermions and will instead form a free Fermi gas (to a decent approximation), which has extremely different properties. That's why it's extremely important that cold-atom experimentalists trying to form Bose-Einstein condensates get the right isotopes of the atoms that they're trying to condense.
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Our current best experimentally verified theory, quantum field theory, isn't based on matter being particles or waves - all matter consists of excitations in quantum fields. The interactions of the quantum fields may appear particle like or wave like, so the wave-particle duality is a duality in the way the fields interact not a duality in the matter itself. The wave-particle duality is just a consequence of using approximate descriptions like the Schrödinger equation, and if we had discovered QFT before the Schrödinger equation generations of physics students would have been spared the confusion.
So wave-particle duality is not down to the fermion-boson distinction. You're quite correct that it's usually experimentally hard to see wave behaviour with fermions, but this is because it's hard to make coherent waves from any massive particles and all known fermions are massive. It would be just as hard to see wave behaviour with bosons, though of course it is routinely done with composite bosons like atoms or even buckyballs.
As Vibert points out, it's no harder to see particle like behaviour with photons than it is with electrons.