I think the difference is degree of intensity. I think I'm pretty safe saying that our view of hell these days is a simple, albeit horrid, pit of fire where bad people are thrown to be with some kind of satanic entity with horns. This doesn't differ too much from Dante's vision and, yes, I agree with litteacher8 in saying that Dante most likely shaped these views.
However, I have some graphic memories of a few of the punishments from Dante's vision, ... such as the one where the people are given a horrid wound, allowed to heal, only to have it ripped open again. I remember the lustful who are made to continue committing the worst parts of that sin over and over, unable to feel love or peace. Or how about the non-rebellious but non-committed. Enotes describes it this way:
These people rush about but never make any decision; their faces bleed from the sting and bite of hornets and wasps and worms devour the blood which drips to the ground.
Can we get more specific than that?
I think that Dante actually shaped how we view Hell. Since the work was so pivotal and foundational, other writers and artists have built on it since. When we think of Hell, our interpretation is somewhat based on this common cultural experience, whether or not we have read the work.
I think that Dante actually transforms the traditional notion of hell in his work. I think that hell is thought of as a place where "bad" people descend and represents a collection of these type of people. What Dante does is to make hell a complex setting, with different degrees and variations. This accomplishes a couple of things. Initially, it transforms hell into a self- reflective experience. As opposed to simplifying hell into a place where "bad" people or "those people" enter, Dante has constructed his vision of hell to be one where individuals reflect on where they would fit. The individual must determine what sins or propensity for sin exists in their own life and examine where they would be placed in Dante's configuration. This reflection and rumination about self helps to make hell a place where true redemption is possible because individuals no longer "demonize" hell as some place where they could not enter. I also think that the classification of disloyalty as the worst of all sins is something that makes hell a different vision than traditionally held. The idea of personal cruelty as being the worst of all sins, the conscious breaking or severing of bonds with another, is something that Dante demands as the worst of all transgressions and something that forces the individual to once again reflect on how they have broken bonds with another. This again transforms what was once seen as hell into something more profound and reflective.