half vertical and half horizontal both share the same resolution.
Just a little notice: there can be a different resolution in vertical and horizontal direction for the same image.
This is the case when the aspect ratio of the stored image is not the same as the ratio of the displayed image.
In particular, this is typically the case for "half vertical" and "half horizontal" formats.
Of course, the resolution has to be understood as number of information units (pixels) per fixed distance in the considered direction. It is often confused with definition which is the number of information units.
The information of depth as we perceive it is stored in the horizontal parallax, thus having a better resolution in the horizontal direction might help to distinguish finer depth details (I did not checked if the magnitude of the gain is significative though).