It is far more likely that the face is a self-portrait, not the devil. Giotto had a prominent nose, and a protruding chin, similar to that of the Assisi painting. The narrow eye in this painting is not sinister, but typical of Giotto's style and that of other Florentine artists of the period.
Renaissance artists often sneaked in "hidden", often caricatured, self-portraits in their works. Another is Michelangelo: in the Last Judgement fresco in the Sistine Chapel, the Apostle Bartholomew is shown holding his flayed skin. Though distorted, the face on the skin is unmistakeably that of Michelangelo.