Vertical dropouts are shorter and stiffer than horizontal ones so the whole rear end stiffens up.
The various roadside cassette removal tools seem to work better with vertical dropouts.
Horizontal dropouts give you better degradation, you can revert to singlespeed in an emergency. It is a bit more effort to remove the wheel and with a wider tyre, you have to deflate to do so.
The modern universal standard is vertical. Only a few traditional builders (such as Bob Jackson) supply the horizontal as standard on tourers.