It mostly works off Morpheus's story of who he believed the One was, and who Neo was a reincarnation of; and how Smith much more accurately fits the description
Neo is +1 and Smith is -1 is the general summary I've seen. To have balance you need to have equal opposites, etc.
Anyway, I've seen The Matrix dozens of times. There's so much awesome cinematography in it that every scene for me is just awesome. Most of it is known trivia but there are some things that are less trivia and more technique-ish. Like when Neo says "There is no spoon" and shoots the elevator cable, the camera is fixed on them while they rocket through the elevator shaft, making it look like the elevator shaft is actually moving around them (which it is, since none of it is real). Stuff like that is why I love the movie so much.
My favorite bit of trivia about the cast is that the "There is no spoon" kid made the final round of auditions for the titular Harry Potter. Instead he ended up not doing much.
Another fun fact is that Connery turned the role down of Morpheus because he basically didn't understand the movie and why anyone would like it. After seeing the success it had, he decided he was going to take the next script he was offered where he had a similar reaction. That ended up being The League of Extraordinary Gentlemen which had horrible reviews. He hasn't appeared in a new movie since.
My problem with the Matrix Trilogy is that Neo's gift is his ability to manipulate the Matrix without being limited by rules. After the first movie, Neo should be omnipotent within the Matrix but in the sequels he is powerful but still limited. It kind of takes the shine off the last two for me.
He fends off literally hundreds of Smiths which would be the equivalent of Superman fending off hundreds of super villains. I guess he's limited in the sense that he can't explode people with his mind, but part of that has to be attributed to the machines/programs also being virtually omnipotent themselves. If Neo was able to do that, the agents would have to be as well, and then we're right back to square one.
Having said that, the second and third movies weren't very good. I mean I guess they were alright but there's no way they stand up to how good the original was. I have a hard time rewatching them while I'll basically watch the original any time it's on TV.