DMC1 was very much an action adventure game. There was equal focus on both the combat as well as the stage design, characters, encounters, etc. Sure it was still cheesy as hell (just like how RE and Onimusha were too), but it's a very different overall package from the "rest" of the series.
DMC2 is just a bad game. DMC3 and DMC4 is when the series got the reputation for being a purely combat mechanics driven game where the regular enemies are ragdolls to test your moves on, the boss fights are the real deal, and the stage design can be kinda annoying. DMC4 was also kinda a bad game, even with good combat mechanics.
From the reviews so far and impressions from people here who have played it, it sounds like DmC has a pretty different balance of focus too. Instead of being totally combat driven, the combat is supposedly feels great, but some enemy mobs and the bosses are all more gimmicky fights than actual combat challenges. There's also a lot of emphasis on art direction and making the backgrounds and environments stand out as you play the game. Certainly a different experience from DMC4 from the sounds of things.