Not good as DMC3
Bosses are not as interesting as DMC had before, they all say uninspired cliche lines we heard a million of times before. You will also be fighting them about 4 times each per single playtrough, so it really gets repetitive. The dice idea is simply horrible and should not have been included, once you learn how to manipulate it, it only becomes a waste of everyones time and breaks the good pace.
Many of the locations simply do not make sense, like for example you are in a beautiful city and the weather is nice, then you stroll down the path and go through a cave about 10 meters deep, and suddenly you're on a snow covered mountain, then you go on and in another cave that's long about 20 meters and suddenly you come out in a tropical jungle that stretches as far as the eye can see.
Sure it looks better than DMC3, but it isn't designed as well. Although Vergil does play a relatively small role here, he isn't even mentioned once. Talk about fan service. Cool and over the top combat cut-scenes that DMC3 made so good seem to be missing here. DMC4 could have benefited from a deeper story and a better cast, especially the final villain.