After training with local sculptors, probably his cousin Johann Peter Heel (1696–1767), Babel spent his journeyman years traveling in Austria and learning wood and stone sculpting techniques.
The choir sculptures (1746–47) elaborately illustrate the death of Christ and display an uncommonly rich variation in clothing forms, influenced by the work of Heel and Carloni.
The main work of the middle period of his life are the side altars of Our Lady's Chapel in Oberarth (1764–67), considered the most valued Rococo furnishings in Central Switzerland.
These furnishings, and those in the palace chapel of Hilfikon illustrate Babel's principal accomplishment: the transformation of Late Baroque templates into a more controlled, constrained and comprehensive form.
His last major work, the 1794 statue of John of Nepomuk on the Devils's Bridge in Egg (Einsiedeln), based on a 1760 bozzetto, illustrates his unwillingness to fully adapt to the new style.