For both of them we see equanimity in the places they encounter the devil--the places where the devil stalks them.
During the night before the Buddha's enlightenment, Mara (the devil), gave Gautama his best shots, over and over. This was the night that Gautama was finally able to see the ultimate emptiness of Mara's threats. This is famously recounted as Mara's armies flinging spears and swords and arrows at the Buddha and the Buddha, recognizing the devil's tricks, turning them into flowers. Gautama recognized that the power of Mara's arrows came from believing in their solidness. Take that away and what's left?
In the Buddha's story--flowers are left! Flowers of joy and peace and gratitude.
When Satan comes to Jesus in the desert (tempting him to break his fast by turning a stone into bread, to prove God's deliverance by jumping off the temple, to inherit the Kingdom of Earth simply by worshiping Satan) Jesus meets each temptation simply with words of wisdom from the rich tradition of God's word. And the devil leaves.
Both Mara and Satan leave, beaten.
Both Mara and Satan leave, biding their time for the next opportunity of devilishness.
Both these stories are about turning points. Celebrations that once a person realizes how the devil works, the rest is just...remembering how the devil works, and working with, deepening, embedding that wisdom.
Remembering the ever-present possibility of equanimity--of grace and peace under pressure.
Our work is to remember the delicious possibility that in the very next place we experience any of the signs that we do NOT have peace--anxiety, fear, hostility, loneliness, despair, jealousy, self-doubt, etc., it's just the devil come again forcing us (inviting us!) to remember that equanimity can be practiced, cultivated, and regularly experienced.