This video shows some of the big differences off: https://www.youtube.com/watch?v=VDAiYc_sy8A&t=2m00s
The big thing is that your abilities in Ninja Gaiden 2 are balanced around fighting large amounts of enemies at once. In Sigma 2, they lowered the enemy count and compensated by increasing enemy health and strength, but since your moveset is basically the same, the game's balance gets thrown off.
Yeah, the biggest problem with Sigma 2 is at the very least, Hayashi and Team Ninja knew where to make changes based on common complaints, but did not know how to properly implement or balance things.
When trying to answer incendiary spamming, he not only lessens the total amount of enemies in encounters (Sigma 2's version of the return to Hayabusa village is absolutely notorious in how overboard Team Ninja went with this), but he ends up opening the door to some very strange balancing decisions (fucking one-hit kill grabs, due to the decreased enemy count, crowd control weapons like the Windmill Shuriken have drastically reduced effectiveness). Team Ninja decides to remove or alter some bosses (no one liked the Tunnel Worm in South America, and Gigadeath was near flat out broken on higher difficulties)... but then decides to add giant statue bosses that no one likes fighting. I don't even know about removing the Tests of Valor outright either.
And I guess to spice things up, he adds additional scenarios for characters where their playstyle is at least fun (Ayane and Momiji), but didn't get the memo that no one wants to fucking play as Rachel (where enemies and bosses a like can be stunned and subsequently recover faster than Rachel can swing her weapon).