According to Callow, the crucial common element between the pair is that they were both flawed human beings. "Dickens was a tremendously open and largely affable person, except in certain circumstances - most famously with his wife," he says. "For reasons we can comprehend but not admire, he began to feel that she was a burden on him. She was crushing his spirit and prohibiting his freedom. He therefore turned against her in a big way. Maybe that's the point where he and Shakespeare connect most completely, because Shakespeare was no stranger to such emotion. The thing is, Dickens was always in denial about things like that while I doubt that Shakespeare was ever in denial about anything."
With this year marking the bicentenary of Dickens' birth, we have seen the publication of several biographies, including Claire Tomalin's much vaunted Dickens: A Life, which concentrated on the author's troubled childhood and marriage. In contrast, Callow has chosen to highlight the importance of live performance to Dickens, an aspect of his character that has inevitably been overshadowed by the ubiquitous popularity of novels like David Copperfield and A Christmas Carol.
"Theatre was vital to him," says Callow. "There's no question that his great contribution has been his books but, for his personal pleasure and needs, theatre was absolutely central to him."
The past 12 months has also seen two screen versions of one of Dickens' best-loved books, Great Expectations. Starring Ray Winstone, Gillian Anderson and David Suchet, the BBC's small-screen adaptation was shown in Britain earlier this year. Meanwhile, One Day author David Nicholls and Prince of Persia director Mike Newell's big-budget production closed the London Film Festival and featured Helena Bonham Carter as a particularly manic Miss Havisham and Ralph Fiennes as a scenery-chewing Magwitch.
"It's a very accessible book," says Callow. "It's a haunting story and it's much less complex than Bleak House or Little Dorrit. There's a clear narrative you can easily connect with and some very strong characters. It's extraordinarily resonant and pretty much everyone can get that. But when people ask me which Dickens book they should read, I always say David Copperfield. But they tend to struggle with it, as it's long and complex. It was painful for Dickens to write and that shows in the writing. In a sense, Great Expectations recycles that story of a young man growing up and it's also full of pain but it came more easily to Dickens."
With the BBC also turning his unfinished final novel, The Mystery of Edwin Drood, into a two-part series, Dickens' stories are now experienced more on TV and film than read.
"That's inevitable as we live in an age that is so very much less literate than Dickens' own when people liked to have books for everything," says Callow.
"People often ask me what Dickens would be doing if he was alive today and I think he would have been a film-maker. He wouldn't have had trouble adapting to a completely different medium because he was such a genius, although it's hard to imagine how you can transfer a person across two centuries. To him, reading was the absolute key to the world and he ate books up. He was always referring to other writers like Shakespeare."
"Dickens" met some famous time travellers when Callow appeared as the author in a Doctor Who episode in 2005.
"That was thrilling to do because he's such a thrilling man," he says. "There was a wonderful scene where Dickens realises that the Doctor knows his books very well and he sort of melts. The final scene moved us all when we did it, as Dickens says, 'you seem to know an awful lot of things, Doctor. Tell me: will I be remembered in times to come and if so for how long?' to which the Doctor replies, 'forever'. He then climbs back into the Tardis and moves off.
"It was a wonderful, extraordinary thought and I can't conceive of how Dickens will ever not be read, as long as people continue to read."
Charles Dickens by Simon Callow (HarperCollins $24.95) is out now.