Python, 8881 Bytes
lambda*x,b="αβγδεζηθικλμνξοπρστυφχψω":(b:="αβγδεζηθικλμνξοπρστυφχψω",x and b or b.upper(),b)[1][x>()]
-6 from TheThonnu for using *
.
-2 from TheThonnu for telling me that the brackets are unneeded.
-28 from mousetail for using an uppercasing function.
-7 from TheThonnu for assigning the greek letters to a variable.