Charles Dickens certainly doesn't get the same level of respect as the Bard, but, for that matter, no one does.
In the USA, you might expect to have Walt Whitman honored on his birthday, but even he - the most universally celebrated American writer - does not compare when it comes to respect, reference, and accolades. Shakespeare takes the day.
But if we are really talking about whether or not Dickens should be given a greater stature in literary circles and wondering why he has possibly fallen out of favor in high schools, it seems to me that the answer is all in the style of his writing. As much as his themes may translate, the prose does not.
That is, of course, only an opinion, offered for sake of discussion.