DmC obviously, but here's why I believe that as such.
DMC1 went on as a B-action J-film. Now I do love J-films and their use of over the top style and presentation, but there are times when it can seem so fake to the common eye. DMC1's story was a bit to cliche and generic at times for a B-movie. It's script and delivery of lines honestly could have been a little better to fit the character's feelings and actions. The story for DMC1 itself is a basic story; go to an island, kill demons, save the world while discovering new things, or in DMC1's case, why does this mysterious woman look like my mother? DMC1's story wasn't the best thing I've seen come out of Japan in terms of story back in 2001, but it wasn't the most awful either. DMC1's story filled its purpose as an event going on and an excuse to have all these cool powers and mechanics. The characters, action, and stylish action came first with the true story being the icing on the cake back in the day. However, I still wished they did better. I mean look at Kingdom Hearts 1 which came out around 2001; it had both story and great gameplay. DMC1 could've had that, but it failed to do so and only focused on looking cool instead of trying to fill out both sides of the game's points.
DmC's story is much more to the early cinematic classic B-movies of action like fight club and They Live mixed with a James Dean-like character whose out to change the world. With DmC, NT focused on actually giving Devil May Cry a story that made sense and was as cinematic as the gameplay. It was filled with good character interaction, a very appealing environment to play in, and some dark elements that gave the feel of suspense. However, its story also has its fair share of flaws like the Angels; where are they the entire game? Or the true affects of Limbo now that its mixed with the real world, will there still be places breaking apart, and what will be the result of the human populace? Will it be like the original series? Questions that could be fixed with either dialog or a sequel. But despite all this, DmC did a better job in putting more meat into the story, however suffered in putting a little less into gameplay when considering DMC3 and DMC4. Naturally it has surpassed DMC1, and dominated DMC2, however in gameplay its one level behind DMC3, but definitely exccels higher in story then 3, and 4. But 4 has DmC beat in gameplay.
All in all, I'm gonna go with DmC because of its actual beauty with scenery, characters are a lot more entertaining to both hear and watch as they go through this demon struggle, the feeling of the game isn't filled with so much anime flash and is more gritty like a Sin City feel to it for me, (and I'm a total Sin City fanboy) it's gameplay was like a movie as well giving cinematic style to the very movements of Dante, the bosses, though easy, were visually interesting and very adding to the story's enemies, and the antagonist was more threatening on both a contemperate level, and a wide colossal level.
I just felt myself more engaged with DmC then DMC1.