Better with heat: granite
The heat thing is the real difference
Almost every practical complaint about quartz traces back to one property: the resin that binds it does not like heat. A pan lifted straight off a burner onto the counter can leave a mark that does not come out and cannot be sanded away. It is not fragile, and a trivet solves it completely, but it is a habit you have to actually have.
Granite came out of the ground hot and does not care. If your household is the kind where a roasting tin gets put down wherever there is space, that is a genuine argument for granite, and it is a better argument than anything about appearance.
Resists stains: quartz
The staining thing runs the other way
Quartz is non porous, so wine, oil, turmeric and coffee sit on top of it until you wipe them off. Granite is porous, which is why it gets sealed, and a sealer wears. On a pale granite, olive oil left overnight can leave a shadow that takes a poultice to draw out.
So the trade is straightforward. Quartz asks you to remember a trivet. Granite asks you to wipe spills and reseal occasionally. Pick the discipline you will actually keep.
Easier to pick: quartz
Choosing the slab
With quartz you can choose from a sample, because the next sheet looks like the sample. With granite you cannot. A four inch chip tells you the color and nothing about the movement, and movement is the whole reason to buy granite. Go to the yard, look at the actual slab you are buying, and ask them to mark where your sink and cooktop will land so you know what the pattern does at the places you will look at most.
Hides seams better: quartz
Seams
Where a run needs two pieces, quartz hides it better because the pattern is engineered and repeats. Granite has to be matched across the joint, and on a stone with strong directional movement a mismatched seam is the first thing a visitor sees. If your kitchen forces a seam in a visible place, that leans toward quartz.