I assume that by hiking shoes you mean robust hiking shoes which are more or less closed (i.e. not consisting of mesh material or the like). In terms of breathability it is also a huge difference if the shoe consists just of leather or fabric or if it has some breathable membrane such as Gore Tex.
If you consider a shoe without a membrane that shall be somewhat waterproof then it won't breathe very much at all as keeping water out in most cases also means keeping moisture in. In this case the only "breathing" –or better ventilation– mechanism is the air that is "pumped" and sucked through the shaft via the movement of the foot within the shoe. for this process you might have a slight advantage if the shoe is lower but I would guess that whenever a shoe reaches to or above the ankle there is significantly less ventilation through the shaft than with a shoe that ends below. With lower shaft shoes you might be able to regulate this to some (small) extent by lacing the shaft not too tight (as long as the conditions allow for it).
With a breathable membrane the driving force is the gradient in moisture and temperature between inside and outside the shoe. This gradient causes moisture to pass the membrane and should be totally independent of the shaft height.
To sum it up: if the shoe has no breathable membrane, a lower shaft might be slightly better, but maybe not so much that you really notice it. For a membrane equipped shoe, shaft length should not change anything at all in terms of breathability.