So here's my personal opinion on Naotora's matchups versus Rig. I might do the others I listed tomorrow or another day. I'll go by your format in which 1-3 equals Naotora's disfavor, 2-2 an even matchup and 3-1 Naotora's favor. I'll also state my opinion matchup difficulty, which ranges from: Very easy - Easy - Medium - Hard - Very hard.
vs.
Matchup rating: 2-2
Matchup difficulty:
MEDIUM
Explanation: Naotora and Rig have a very similar playstyle. They both rely on high strikes in both the neutral game and the stun game to presure their opponents. Next to that, they are both very kick-oriented and have a limited amount of punches. However, the punches they have are actually really good. Both have an amazing 4P, 3P and 8P which lead to very deep stuns. Both also have very high combo damage and great zoning tools. However, since their playstyle revolves mainly around high kicks, they are vulnerabe to high crushes. They also have a similar strike speed in general.
As for the differences, I'll start what Rig has what Naotora doesn't. Rig, in general, is much safer to play than Naotora. Most of his punch strings are safe and his high kicks, like the standard K, even leave him at +1 frame advantage. What's more, Rig has a plethora of kick and punch sit-down stuns which lead to guaranteed setups. 7P is -5 on block and gives Rig a guaranteed 33K launcher! Naotora doesn't really have a lot of guaranteed set-ups compared to Rig. Rig also has two stances which are in general way better than Naotora's Ii Clan stance. It has so many options including safe tracking moves, tricky lows, a safe mid punch, a chargeable mid kick and even a reset throw. Rig has a i12 mid kick which he can use as a counter poke against Naotora's pressure. Mix-ups wise Rig is really dynamic, compared to Naotora who has relatively predictable strings. Last but not least, Rig's environmental game is among the best in the game. There are few characters which have a better environmental game than Rig and Naotora is not one of those characters. For example, Rig has four possible ways to set up a guaranteed Critical Burst by just making good use of the environment.
Naotora however has the tools to deal with some of Rig's trickery. Her 6K is great at range and will beat most of other Rig's spacing tools aside from maybe Rig's 66P. Naotora's 9K and 236K close the gap quickly and have high priority, although they are somewhat risky to use. The important part however is that these two moves can deal very well with Rig at longer ranges. Naotora has a way better neutral kick at 11i which beats almost all of Rig's options. I also believe Naotora's pressure is better in general, especially at the wall. Rig can't sustain his pressure in Bending Stance because a simple 2H+K or 2P of Naotora can effectively shut down all of his options. Naotora's combo damage is probably slightly higher than Rig's as well. Furthermore, Naotora's holds and throws are way better than Rig's. Naotora's 66T does 99 damage on Hi-Counter which is an insane amount of damage, and this is excluding environmental interactions! Rig's throws on the other hand are sub-par and lacking in damage, with the exception of his 41236T which sets up for some nasty follow-ups. Naotora's holds are pretty average but they are way better than Rig's holds, which are probably one of the worst damaging in the game. Rig's low strikes also aren't as good as Naotora's low strikes.
Summary:
- Similarities: Kick-oriented, pressure-based, limited but decent punches, great zoning tools, vulnerable to crushes, similar strike speed in general.
- Rig's advantages: Safer, more and better guaranteed setups, better stances, better mix-ups, 12i mid kick as counterpoke, better environmental game.
- Naotora's advantages: Great spacing tools to deal with Rig at range, 11i high kick to start pressure, better at maintaining pressure than Rig, slightly higher combo damage, better throws, better holds, better low strikes.