Now that I have beaten Ninja Gaiden 3 US, I can now talk about it in full and how it compares to the 1st 2.
I would say this is the worst one due to a lot of changes it had from the Japanese version along with it's other problems like the horrible hit detection. This game has the worst hit detection in the series. There are times when I get hit even when I killed the enemy, there are times where I'm above, behind or below an enemy and still getting hit by them somehow, and my sword would go through an enemy and not hit them so I get a cheap hit in return. Even hitting items can sometimes take 2-4 tries due to how bad the hit detection is. It frustrates me since the game is already hard as it is so that's something that needs work.
Also, the jumping is floaty compared to the 1st 2. You really have to control him more to get where you want to line up your jumps. You will get used to it but it seems to not control as smooth as the 1st 2.
Then we have the level design and enemy placement. It seems like some sections in levels are designed to just frustrate the player more with hazards being in nasty spots than being designed very well. The last level is a perfect example of this as well. Enemy placement is all over the place and for this US version more enemies are added to make things worse. The game clearly wasn't designed around it so that's a change that shouldn't happen.
Worst of all is the fact you pretty much need to die on the last level due to the strict timer it has if you take your time through the level. It's really poor design and the game should had given you more time to get through it normally.
Overall this was a decent game despite it's issues, and the Japanese version sounds better. It has good gameplay, some improvements like no respawning enemies(for the most part)and being able to see items before you hit them, it has the toughest bosses in the series, and the music is good. However the 1st 2 are better obviously. If you are looking for a challenge, play the US version, however, you need to be dedicated to it to beat it because it's easily one of the hardest games I've ever played, and I played Battletoads so yeah!
It took a lot of years, but I'm glad I'm done with that game!