The only reason you might need """ instead of ''' (or vice versa) is if the string itself contains a triple quote.
s1 = '''This string contains """ so use triple-single-quotes.'''
s2 = """This string contains ''' so use triple-double-quotes."""
If a string contains both triple-single-quotes and triple-double-quotes then you will have to escape one of them, but this is an extremely rare situation.