Both are awesome, beloved action games that play to different strengths.
DMC1 has possibly the best level design and atmosphere of any action game even today. I remember the boss' and environments to this day. The organic, heart-like beating trees in the Cathedral. The flying ghost ship. The maze where you get Ifrit. Phantom, Griffith. And Mundus, of course.
DMC3 introduced freestyle combat as we know it today. Make your arguments about which does it best, DMC3, DMC4, or Bayonetta, but the latter two wouldn't be here without 3. Plus DMC3 is notable for being the first and thus far only action game with a good story for those who care about that sort of thing.
Ninja Gaiden is a different kind of beast, with it's rhythmic, tactical combat. It's ball crushing difficulty only entices the player more. It's more memorable as an experience rather than a any single encounter, but it's a gratifying experience none the less.
These three games opened the way for the next gen action games to take place. Individually, they aren't perfect, that should be made perfectly clear now, because I hate how these discussions always have the majority of people claiming one game is 'clearly' better when that shouldn't be the case. Each have different styles and in those styles, they each have their own weaknesses that the others have exceeded them at. To choose any single one of them over the others exclusively is to limit only your own enjoyment of the full spectrum of the glory that is action gaming.
