The claim is that women need more sleep than men because they do more multi-tasking during the day.
Despite the controversy, it's hard to find conclusive evidence linking gender to different sleep needs.
This WebMD article seems to claim that there have been no conclusive results in recent studies, as seen below:
Right now, we don’t even know whether men need more sleep than women, or vice versa. “There’s no nationally representative data [on gender differences],” says Michael Twery, PhD, director of the National Center on Sleep Disorders Research, a division of the National Institutes of Health.
In contrast to that, the National Sleep Foundation does cite yet another Daily Mail article making similar assertions such as:
'Women tend to multi-task - they do lots at once and are flexible - and so they use more of their actual brain than men do. Because of that, their sleep need is greater.'
Last, yet not least, it's interesting to note that there seems to be a stronger correlation between sleep deprivation in women and cardiovascular health problems, according to this Duke Medicine publication, suggesting that there are differences related to the effects of gender upon sleep and health. However, as previously said by Dr Twery, the data is not representative on a national scale, considering there were only 210 test subjects:
Researchers studied 210 apparently healthy, middle-aged men and women without any history of sleep disorders.
Therefore, it is highly unlikely to jump to any conclusions yet.