Another thing I respect Ninja Gaiden 3: Razor's Edge for, is the more honest arcadey nature of the game. The previous two games were already arcadey in nature, but the exploration on top of that in their vanilla releases. Ninja Gaiden Sigma and Sigma 2/Black II pretty much remove most and all of the puzzle solving respectively. It's honestly works to both games benefit. Especially in Black II.
I find it much harder to go back and play DMC4 Dante. He's still fun, but really limited compared to DMC3 incarnation (especially with the Switch port allowing style switching on the fly) and especially to DMC5. I only like 3 out of his 7 weapons (Dark Slayer Style gives him limited uses of Yamato that can be fun, so it counts). Though Gilgamesh is just a worse version of Beowulf, even though I enjoy using it.
DmC_Dante does have more limited weapon kit compared to DMC4 Dante, but at least DmC_Dante's weapons are all fun to use, and switch between combo starters and enders with pause combos to make up for his more limited kit. DmC_Dante still has more robust and flexible tool kit, than most Western style Single Player Stylish Action Games or God of War clones. The Definitive Edition of DmC (2013) fixes most of the gameplay issues I had with the original release, thus making him more fun to play and experiment with.