I played every chapter in Ninja Gaiden II and Ninja Gaiden Sigma II back to back and was pretty taken back by how different the two were.
1. Right off the bat in Sigma, it was very strange to see clouds of purple smoke coming out of human enemies and a Giant Buddha Statue appear out of nowhere and destroy a bunch of skyscrapers before confronting Ryu. Also, the doors/key items not being interactive like in the original took away from immersion. I did, however, appreciate being able to do the Flying Swallow and Izuna Drop right off the bat prior to discovering their scrolls.
2. Hayabusa Village was near identical outside of Rod of Trials removal, but it really highlighted the biggest gameplay difference between the two versions. The projectile weapons. In the original the aiming was manual and could be charged, but the aimbot cursor and uncharged shot in Sigma made it much easier, but less versatile. The number of varied projectile weapons available to Ryu in Sigma was reduced to three that just do different amounts of damage and give infinite ammo.
3. These changes made the city level's Demon Train boss fight trivial. Sigma made very few changes outside of removing enemies from select underground areas and strangely switching the weapon found in the ninja exhibit from dual katanas to a greatsword exclusive to Sigma. But, the Statue of Liberty fight added in Sigma was cinematic and I appreciated early access to the bladed nunchucks.
4. The biggest changes I observed were in the Aqua Capital. Sigma censored the intro with Ryu cutting a Lycan in half and removed the enemies in the water for starters. It also cut enemy numbers and removed some scenic water effects in the fountain and waterfall areas. It even glued Ryu to a small platform for the Ghost Dragon boss fight in the underground caverns and limited him to only using projectiles. It was here Sigma began spamming the limbless floating demons in place of local enemy types. It also did away with the underwater machine gun and gave Ryu an oversized rifle cannon instead.
5. A few other boss fights in Sigma were changed, but not in a way that drastically changed the journey even if a Giant Demon Centipede boss area was erased completely. Though I must admit that the dying detonation of the Giant Lava Amadillo after the airship crash in the original was cheap (required nippo or talisman of rebirth) the availability of explosive shuriken made it relatively easy to replay. I even enjoyed the challenge of the Two Flying Dragons boss fight in the original more than the single Grounded Dragon boss fight in Sigma and found the Two Giant Lava Armadillos were less annoying in the original than Super Bephomet with his erratic invincible flight patterns in Sigma's venture through hell. In later parts of the game, I even slightly appreciated the removal of waves of rocket launcher spam enemies, flying enemies, and the abbrevited passages through tunnels and segments of hell in Sigma but not enough to ignore the reduced enemy variety.
6. The coolest parts of Sigma are in the addition of Rachel, Momji, and Ayane as playable characters (though, Rachel's chapter is the worst of the three) and being able to use everyone in the Ninja Races and varied Tag Missions in addition to replaying any chapter.
TLDR: In the end, my opinion is that Sigma 2 is far from the definitive version of the game, but should I want a taste of Ninja Gaiden's second installment it will likely be the version I revisit as it has so many more features. However, should I want a full course meal, the original has no substitute.