That depends on the hackmore!
For example, these first two hackamores apply pressure to similar areas:
And these third and fourth hackamores apply pressure to similar areas, different from the other two:
What it all boils down to is where the noseband, curb chain/leather, and cheekpieces attach in relation to one another, and to a lesser extent, where the reins attach.
Take this for example:
I've drawn over these pictures to make this a little simpler to explain. Notice how with these, images 1 and 2, the basic structure of these two hackamores is very similar. The noseband, cheekpiece and curb chain are all fixed to the hackamore cheek, with relatively equal spacing.
The basic mechanics of this structure is: when pressure is applied to the reins, the hackamore cheek, or 'shank' if you will, rotates the upper structure, hinging off of the noseband. This pull the cheekpiece up and forward, putting pressure on the poll, and the curb chain back and up, putting pressure on the jaw.
The fact that in Image 1, the hackamore cheek is 'fancy,' for lack of a better term, is irrelevant. It doesn't affect where the reins attach in relation to the rest of the mechanism.
Therefore, the shape of the hackamore cheek, for this type of hackamore, largely does not matter. Now things get interesting!
In Image 3, you'll notice that the cheekpiece and noseband are attached, and the hackamore cheek and curb chain hinge off of it.
This means that when pressure is applied to the reins, the hackamore cheek moves back, pulling the curb chain up, applying pressure to the jaw and nose. There is no pressure on the poll, however, as the noseband and cheekpiece are fixed, and outside of this hinging action.
For this hackamore, the shape of the cheek matters as much as where various straps are in relation to one another. Again, the slight jog in the hackamore cheek is ornamental and inconsequential as it doesn't affect where the rein is in relation to everything else.
Now on to Image 4:
For this hackamore, the shape of the cheek matters a lot. Also, it should be noted that this is known as a little s hackamore, not just your run-o'-the-mill hackamore.
The mechanics of this hackamore are as follows. When pressure is applied to the reins, the entire hackamore cheek hinges up and back. Because of where the cheekpiece is attached, this actually relieves
pressure to the poll, while applying pressure to the nose and jaw. So in conclusion:
The shape of the hackamore cheek usually does not affect the action of the hackamore. Get as ornamental as you like. Just look carefully at where all the various straps (noseband, cheekpiece, curb chain, reins) attach in relation to one another,
and understand the basic mechanics of such structures.
End note: none of these images belong to me.