Lent and Advent, of course. That question should probably have been better worded as, "Do Easterns regard Lent and Advent as penitential seasons?"
Great Lent is pretty much penitential across the board: West, East, and more East. Advent, on the other hand, isn't really penitential in the same way (on this point, I think I can speak for both traditions, at least in their Orthodox manifestations).
A more useful discussion might center on the question of what "penitential spirituality" is and how it differs in Roman Catholic and Orthodox traditions.