From what I can tell, they can represent their country in both contests but they can not win both.
So, if someone goes to the Miss World competition and loses, she can then also go to the Miss Universe competition.
However, if she were to win the Miss World competition, she would not later compete in the Miss Universe competition because her duties as Miss World would prevent her from winning, so they send the first runner-up to compete in her place instead.
Here's an actual example:
On December 14, 2014, Miss South Africa Rolene Strauss was crowned Miss World in London. But unlike in other countries, whomever is chosen Miss South Africa in any given year represents the country in all major international beauty pageants, including Miss Universe, Miss International, Miss Supranational, Miss World and Miss Grand International.
So, when the Miss Universe Pageant is held in Florida next month, Strauss will take to the stage as Miss South Africa, right? Wrong.
Remember what the Miss Universe Pageant hosts always say before announcing the name of the new Miss Universe? “In the event that the new Miss Universe will not be able to fulfill her duties, the first runner-up will automatically become Miss Universe.”
Ergo, Strauss as the reigning Miss World can’t possibly fulfill her duties as Miss Universe which include traveling and appearing with Miss Universe Pageant owner Donald Trump. So Strauss has been disqualified from the Florida pageant.
Miss South Africa’s 1st runner up, Ziphozakhe Zokufa will take over to represent her country in the Miss Universe Pageant.