月 refers to the duration aspect of a month, i.e. one 月 is a time span of 30 days.
月份 refers to a particular point or period of time in the year.
What confuses people is they both can be used to express 'month N of the year' and are completely interchangeable in this usage. E.g. 四月 = 四月份 = April.
But to show the difference, imaging there is a festival called 'jogger's month' when everybody is supposed to keep jogging everyday during the festival. It lasts for about 30 days that's why it's called a month, but it may start at a different point of time every year. In this case, you can say: 慢跑月每年在不同的月份举行。去年是在四月(份)，今年将是在九月(份)。
For the sentence in your question, if I understand correctly, Ramadan is actually the name of a month on Islamic calendar, so both 月 and 月份 are correct. 月份 would give people slightly more hint on it's at the same time every year, while 月 merely indicates the length of the period.
Some discussions on 月 vs. 月份 as FYI.