I have some very hard pills, and scoring them just doesn't help that much. The way I split them works better:
Start by scoring the pills. Next, straighten out a staple, paper clip, thin nail, or piece of wire, and tape it to the table so it doesn't move around. Place a pill on top of the wire so it's balanced, scored side up, with the score going right over the wire. Press down on each side of the pill with your thumbs. The wire acts as a fulcrum and the pill splits.
To make this easier, there are two possible improvements. First, you may noticed that the pill won't balance on the wire unless you hold it. This balance problem may be remedied by providing a flexible but flat surface for the pill to sit on. Lining the wire on each side with a paper towel (folded in half if needed) is sufficient. The paper towel will act as a flat surface which can hold the pill, but when you apply force, the tissue will compress but the wire will not. The pill still breaks.
You may notice that for a small and hard pill, it's still difficult to apply enough force without hurting your thumbs. If you have a wooden dowel or thick stick and a saw or sharp blade, you can cut a notch into one end of the dowel. Press the dowel down into the pill so that the notch is over the score, protecting it from force. All the force is directed at the sides of the pill. When I press down on the dowel, the pill usually snaps quite easily.