Butter gives pancakes better dairy flavour and attractive browning, while oil makes pan temperature easier to manage across a large batch. You can use either in the batter and either on the cooking surface, but those are separate decisions.
Fat in the batter
Melted butter adds flavour and milk solids. Let it cool before whisking it into milk and eggs. If the liquid ingredients are very cold, the butter may form small flecks; room-temperature ingredients produce a smoother mixture.
Neutral oil disperses immediately and keeps the pancakes soft even after cooling. It is useful in dairy-free recipes and batches that will be reheated.
To replace oil in the batter, use the oil to butter converter and choose melted butter. To replace butter with oil, use the reverse converter.
Fat on the pan
Butter browns quickly and can leave dark milk solids on the griddle between batches. That first pancake may taste excellent while later pancakes pick up burnt specks.
Neutral oil gives more consistent colour because it contains no milk solids. Apply a very thin layer with folded kitchen paper or a heatproof brush. Excess fat fries the edges and creates patchy surfaces.
A practical compromise
Use melted butter in the batter for flavour and a thin film of neutral oil on the pan for control. This separates the flavour decision from the heat-management decision.
Alternatively, wipe the pan clean between batches and add a fresh small amount of butter each time. That works well for a short stack but becomes tedious for a crowd.
Read the surface
Cook pancakes over medium heat. Flip when bubbles rise and remain open, the edges look set and the underside is evenly golden. If the butter turns dark before those signs appear, the pan is too hot.
Butter is the stronger flavour choice; oil is the more consistent cooking fat. Using one in the batter and the other on the pan often gives the best result.