First of all: who was the monster that ranked it as "average"?
That said... I played NG Black years after its release, only after I bought a XBOX 360 in 2011 (the game is fully retrocompatible with no issues). It was one of the games from the original XBOX that I was interested in (the others being Panzer Dragoon Orta, Phantom Dust and Jet Set Radio Future), but my interest was mostly on the name recognition alone: I didn't know anything about this game, except that it was well reviewed and considered a worthy successor of the NES originals, which I loved as a kid.
My mind was blown. First of all, the graphics held up really well: the game was in widescreen and running at solid 60 fps, with very clear textures and models. Not only that, the art style was very appealing: the scenery was very lush and colorful, going for a mix of realistic and animesque art style. Then, as soon as I got to the first enemy ninjas, I felt how good the combat was: Team Ninja pretty much used an engine that would fit well in a 3d fighting game, something that, until then, I had only seen implemented well in Shenmue. But, most importantly, the combat wasn't based on just juggling your enemies and locking them on infinite combos: it was based on movement, defense and counter attacks. This is what makes NG completely unlike its competitor at the time,
Devil May Cry: while the later is based on the idea of being stylish (chaining long combos and different attacks together), the former is all about being pragmatic, killing your enemies fast with a few precise attacks. I vastly prefer this approach to combat: you keep defending, moving and observing; as soon as you see an opening in your enemy's strategy, you kill it in a few hits.
So, I was pretty much sold on the visuals and the combat. But the game is definitely not just that: the very first level already shows the player that there will be some exploration and platforming to do. This is only fully realized after you get to the city of Tairon in level 4: from this point onwards, the city works as a fully explorable hub that you open more and more as you complete new levels. Alas, what makes the exploration great are the platforming elements: they're very similar to
Prince of Persia: the sands of time, which means Ryu can jump, run on walls, swing on bars and hang on ledges. These are all combined to make some challenging platforming sometimes, which is good to break up the pace and not make the entire game just about fighting. There are also a few puzzles through the game, but none of them are very complex and they're all solved just through exploration (a good thing in an action game).
The enemy variety and their attack pattern is another important thing. Even the first enemies in the game are already challenging (none of them will stay in one place waiting to be sliced), and the game will throw more and more different mooks on your way: each of them have different attacks patterns and must be dealt with distinct strategies. Especially when you get good at the game and play it on the harder modes, it gets obvious that there's not a single weapon/combo that works on most situations - my last playthrough on very hard made me think a lot about which weapons and attacks to use in each encounter, which is even more evident on bosses. This is a game that just can't be won by button mashing, even on normal mode: every time I thought "hey, I'll just attack and see if it dies before me" I got a game over screen.
Now, especifically on Black, there is one more thing to point out: the way it does the different difficulty settings is just perfect. As I commented on another thread, most games will just transform the enemies in either bullet sponges or in perfect AIs. NG Black, on the other hand, doesn't change the enemy's stats too much (besides them hitting harder): what it does is rearrange the encounters (throwing harder enemies at you earlier) and, most importantly, it includes entirely new enemies - and even bonus bosses! I think this was the first game that made me appreciate playing on hard (and later very hard... not master ninja yet), as I wanted to see everything the game had to offer.
As it was mentioned earlier, there are also unlockables: NG includes the original NES games, while NG Black brings the more obscure arcade game (it can even be played in coop!). Both of them have different costumes, purely cosmetical stuff. Besides that, NG Black also has challenge modes, including a new, very short campaign that presents two new bosses.
I never played the Sigma version, but, from what I understand, most of the criticism comes from the mandatory Rachel levels (it seems she is slower than Ryu, so some people dislike having to play as her) and the slight rearrangement of some things, like a few puzzles being taken out. I've also read some comments stating it is a slightly easier game than Black, and I can confirm that the videos I saw from the special challenges looked much more manageable. Still, it has even better visuals and new stuff (I wouldn't mind the new levels with Rachel), so it's not necessarily inferior to Black. (Just to clarify: Black is a rerelease of the original, fixing some problems - like the camera, which was not even fully controllable before - and adding new weapons, enemies, challenges and difficulties, so, besides it not having the NES games as unlockables, it is a huge upgrade over the original release.)
About the problems, the only thing I can point out is the camera: it's not really bad, but the game is so centered around movement that the camera sometimes will not be positioned optimally. When you get good at the game, that's generally not a problem, but until then, expect to be angry at it. At least the game has the decency of taking some measures about it: as I only learned during my very hard playthrough, the enemies will only attack when the camera is showing them - I even exploited this to beat the second boss and the goddamn Berserkers.
I would even talk about how awesome the story is (albeit extremely concise), but
spidershinobi does a much better job than me regarding that, as he got some of the finer references. So, all in all, it may not be a perfect game, but the sum of its parts makes it one of the best things (if not the best) I've ever played. Man, I love this game. I hope Tecmo-Koei hasn't stopped porting/rereleasing it, as I would love to see it on current consoles/pc.