Vertical
I'm outvoted by a longshot here, but most of the time I split vertically. Most of the rounds I have are enornmous, and lifting them atop the beam would be almost impossible. More important, about four years ago I tried working too fast while horizontal and somehow got my left hand between the log and the foot of the splitter (my splitter's wedge moves). That broke three bones in two fingers on my left hand. They healed, but it scared the pea out of me.
Splitting vertically, I have never injured myself. To make it more comfortable, I have a dedicated and strong old chair that I sit on rather than kneel. It also seems that I have more control of the wedge position and the size of the split log when splitting vertically.
However, to each his own.