For menu, we typically use "ο κατάλογος". το μενού can be used, but it isn't as common. το μενού tends to also be used to identify "combo" meals at restaurants, too. I don't have a preference, just a comment...
That is true but I believe it is the preferred and more widely used word for menu. Μενου is a westernization that has entered into the language over the years.