It's hard to say because different readers at different times have responded more to one rather than to another. In the 19th century, 'The Pickwick Papers' was incomparably popular, and 'Pickwick' is a book that is much harder for people who aren't familiar with Victorian literature generally, or with other Dickens work, to come to terms with today than it was a century and a half ago. 'Barnaby Rudge' is probably the one that is least read and written about.
I think in some ways the key to answering this is to look at the reception that greeted 'The Old Curiosity Shop' and the story of Little Nell. When it first came out, it hugely increased Dickens' readership, there are anecdotes about people weeping at her death, of crowds gathering at the docks in New York when the ship was coming in with the latest instalment, shouting out 'Is Little Nell still alive?' It may be apocryphal, but it's part of Dickens lore.
But by the time Dickens died, in 1870, people were wondering what all the fuss was. Attitudes towards sentiment had changed very considerably. By the end of the century, when his kind of fiction had very much gone out of favour, and writers like Joyce and the Bloomsbury set were coming in, Dickens was very passÃ©. Oscar Wilde made the most famous comment at Dickens' expense when he said that one must have heart of stone to read the death of Little Nell without laughing.
"Oscar Wilde made the most famous comment at Dickens' expense when he said that one must have heart of stone to read the death of Little Nell without laughing"
When I was an undergraduate, which was more years ago than I care to remember, it was still really not respectable to like 'The Old Curiosity Shop'. And yet, with the changing climate of the times in the 1960's, when youth culture and melodramatic attitudes were much more up front and open, moving away from subtlety and stiff upper lip, it started to come back. It's probably the book I've worked on most in my career. When I started working on it, it was very unfashionable to do so, but it's certainly widely well considered today.
We could also look at 'A Tale of Two Cities' which has never had a particularly strong following among academics but, if it's not the most read it's certainly one of the most read of all of Dickens' titles for the last century. I've been working for 20 years to produce a scholarly edition of 'Sketches by Boz' which is a collection of short stories and pieces which really launched his career in the 1830's and led to him getting a contract to write 'The Pickwick Papers' and the rest was history. By halfway through his career Dickens thought of it as juvenilia and, by and large since the 1830's, they have had very little attention. What my own work is trying to demonstrate is, first of all, that they made a huge impact and, second of all, that they really are worth paying attention to because many of his characteristic touches and stylistic devices are all there to be found in the sketches.
Illustrations from A Tale of Two Cities, from left: Lucie Manette finds her father in The Bastille; she faints as Charles Darnay is condemned for the actions of his ancestors, based on a letter from Dr Manette's old cell