WWII is the key event of the 20th century. For good or for ill. A small but growing coiterie of historians on both the far right & the left are beginning to question its necessity. What they also have in common is ascribing the war to Churchill.
I'm always trying to expand my horizons, but keeping in mind that Man of the Century is about influence & only influence, I still think Churchill would have been a solid choice.
Both Gandhi & Mandela might be choices for the 21st century, depending on India's continuing influence on world affairs, technology, science, etc.. Mandela, if democracy spreads throughout Africa & the nations there develop as emerging powers.
Dalai Lama...? I just don't see being particularly influential. Unfortunately Tibet's indepedence appears to be a thing of the past.