Sept 16, 1963 was the day the Federation of Malaysia was born, after Sabah and Sarawak joined Malaya (Singapore, too, but it went on its own on Aug 9, 1965). Malaya gained its Independence from the British on Aug 31, 1957.
An so, it will always be a bone of contention. Is Malaysia 44 or 50 years old? [read this Borneo Post article here].
I say Sept 16 should be celebrated just as grandly as Aug 31. Sept 16 is our National Day (as that's when we became the nation that we are today) and Aug 31 our Independence Day (and that's when we should Merdeka, Merdeka, Merdeka).
Happy National Day, Malaysia!