Not intending to launch a battle between these two U.S. holidays, I'd like to reduce the confusion between the two. They have different, distinct purposes.
As described in Garbl's Editorial Style and Usage Manual:
Memorial Day Capitalize the U.S. holiday for honoring men and women who died while serving in the country's armed forces. Since 1971, it's been celebrated the last Monday in May. Memorial Day was originally called Decoration Day, which commemorated the sacrifices of Civil War soldiers. For the holiday honoring men and women who have served in the U.S. armed forces, see Veterans Day.
Veterans Day Capitalize. No apostrophe according to the U.S. statute establishing the legal holiday to honor all men and women who have served in the U.S. armed forces. Since 1978, it's been celebrated on Nov. 11. Veterans Day was originally called Armistice Day to honor people who served in World War I. The U.S. Department of Veterans Affairs, formerly the Veterans Administration, also takes no apostrophe. For the U.S. holiday honoring men and women who died while serving in the country's armed forces, see Memorial Day.