I'll start by saying I don't understand the term "property dualism" as you're using it. So this only addresses what is meant by hylomorphism -- which is properly speaking neither dualistic not reductionistic.
You can roughly trace two basic traditions of philosophical thinking: one idealistic and one empirical. Using this rough sketch, we have the following pairings:
Idealist: Plato | Descartes | Kant
Realist: Aristotle | Locke | Hegel
There's a lot more that could be added to the picture, but these are important pairs.
The thinkers in the above category tend to posit views that we can understand as somewhat dualistic in nature. Plato famously calls the body a trap for the soul. Descartes' confidence in the mind is much higher than the body. Kant's philosophy centers on giving us a faculty that makes us free despite the determinism in the world.
The thinkers in the below category are more positive about the body (for now let's leave out some of the complexities of saying this about Hegel. Thus, while for Plato, the body is the trap for the soul, for Aristotle, the soul is the principle that organizes the body as the sort of thing it is (here following Sir Anthony Kenny's definition provisionally).
It's important to realize that for Aristotle, every living thing has a soul (but no everything has an immortal soul).The way he means soul is not a religious concept per se (though it was adapted to be one by Muslim and Christian thinkers later).
To give a clear example, the form of a giraffe (i.e., it's soul) is what makes the difference between having a giraffe in front of you and a pile of matter composed of the same elements that would make a giraffe but are dead. (This is an image from Thomas Nagel). Again, "soul" here means precisely this difference. It's not some further difference on top of all the processes that lead to this matter being organized and sustained giraffe-wise.
To put it another way, if we kill the giraffe, nothing is organizing that matter giraffe-wise anymore and over time it will break down whereas as long as the giraffe is alive, the whole giraffe is organized and continuing as certain type of living thing.
As a theory in philosophy of mind, the idea of hylomorphism is that it's a mistake to view brain as identical to mind, because mind is something that occurs not just when certain matter is present but precisely as an organizational process that orients all of the activity of brain-wise matter and neural networking in a mind-wise way. Thus, it's not any standard sort of reductive materialism about mind, because it asserts mind is more than matter.
Conversely, hylomorphism thinks its a mistake to view mind (at least human mind or animal minds) as possible apart from matter organized brain-wise. Thus, it's no dualism because it does not think mind occurs without this organizational activity occurring over the right sort of matter, i.e. brain.
For more, see William Jaworski's index of terms.