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The problem is the winter freeze/thaw cycle. Mortar and/or concrete has no flexibility. When the soil expands and contracts, the mortar snaps. You get around that by putting it on a surface that is not going to move with the freeze/thaw. That means a steal reinforced concrete slab for flat work and a poured concrete footing that goes below the frost line for walls.
This is the reason that modular block walls are so popular - they flex with freeze/thaw without breaking, so you don't need a concrete footing below frost line.
If you want to use stone and don't want to deal with the extra work and expense of the concrete, dry lay the patio and dry stack a complementary stone wall. You will regret the two options you have listed as soon as you get a real winter. They will break up, it is just a matter of when.
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