You can't judge which is better until drive on both games
Start from simple stuff, does the ND MX5 in AC has properly simulated rear torsen LSD ? ND Miiata with rear open diff or optional torsen LSD drive differently. Which also my curiosity with the Hot Version vid, does the stock ND in the touge run has LSD ?
For GT6, an NC Miata uses CM tire to get to grip level of stock road tires, and even that still very grippy IMO, it needs effort to slide it on CM. GT5/6 have always fitted one or 2 level grippier stock tires, which was my question to Nasanu, if he used comfort tires or sports tires ? It should show on the HUD like in GT6 if I'm not mistaken. I'm leaning on CS or CM as stock, if PD is trying to be more realistic.
As for oversteer and steering correction, even at low speed in real FR car, you may need correcting a lot if driving at around 80-120 kmh on typical suburb roads, road imperfections, dust, weather etc can make good stable sports car twitchy. It really down to how a driver drive, as well as road/car condition.