Sheen prefers characters who are more of a cipher, the 40-year-old actor said in an interview at September's Toronto International Film Festival, where his soccer drama "The Damned United" played in advance of its theatrical release Friday.
Elizabeth and Nixon, "these are characters who don't have as much ability to cover up, so they're more transparent in some ways. So you kind of know where you are with them as an audience," Sheen said. "Whereas with the Blair character, the Frost character, it's harder to know what's really going on for them. That's what I find interesting as an actor."
In "The Damned United," Sheen plays British coaching legend Brian Clough during his short, disastrous tenure at Leeds United, the championship team he took over from a bitter rival in 1974.
Clough, who died in 2004, was a polarizing figure for British sports fans, always ready to laud his own talents and criticize opponents.
"When he came on the TV, people either hated him or they loved him, and even if they hated him, they still couldn't help but just laugh and be entertained," said Sheen, who considered pursuing a soccer career before he took up acting in his midteens. "I always found him quite sort of an unsettling figure when I was a kid, because I think even then, I could sense that there was a real anger in him."
Born in Wales, Sheen studied at London's Royal Academy of Dramatic Art and went on to acclaimed stage performances, including the title role in a 1999 revival of "Amadeus" and the Frost role in the original production of "Frost/Nixon."
Sheen made his movie debut in Stephen Frears' 1996 Jekyll-and-Hyde tale "Mary Reilly," working with the director again as Blair in the TV movie "The Deal" and "The Queen." He plays Blair a third time in the upcoming drama "The Special Relationship," about the prime minister's bond with President Bill Clinton.
Other screen roles include the werewolf Lucian in the "Underworld" franchise, whose first two installments starred former girlfriend Kate Beckinsale, with whom Sheen has a 10-year-old daughter.
Sheen also plays the White Rabbit in Tim Burton's upcoming "Alice in Wonderland" and co-stars as vampire leader Aro in "The Twilight Saga: New Moon."
His initial research for Aro came close to home. Daughter Lily is a huge fan of Stephenie Meyer's "Twilight" novels.
"I wanted to find out about the character without having to read the books immediately, but I couldn't tip my daughter off, because that would get her overexcited," Sheen said. "I said to her, `Oh, Lily, these books you're reading. Someone was talking about them the other day. Is there a character called Aro in them?'
"She said, `Yes, he's the head of the Volturi. He can tell what people are thinking just by touching them. Are you going to play him?' I went, `No, no, no, no,"' Sheen said, laughing. "It was hilarious. And then of course, once I knew I was going to do it, I still couldn't bring it up with her until the deal was done, because if I was to say, `I'm going to do this' and then it didn't happen, it would have been horrendous."