So I put some figures together. First up, the steering angle vs. yaw rate and yaw acceleration. Yaw acceleration is calculated as the derivative of the yaw rate (with respect to time), filtered down to 3 Hz. The reasoning behind that will be explained later.
1.
Here it can be seen that the yaw rate is cleaner. Note the steering input is more steady in the low frequency range, but has more high frequency adjustment in general. The acceleration looks a bit of a mess, and will be discussed in more detail later. At 1500 ft, there's the split-mu oscillation - the car gets two wheels on the dirt at turn 2 and a dab of opposite lock is applied - the oscillation is independent of that steering input. This is fascinating in its own right, but not relevant here.
2.
Whilst that is enough to get an intuitive sense of the input / output behaviour, next up is an FFT of the yaw rate and acceleration. It is a representation of the contribution of each frequency to the overall picture, so it can be used to infer how stable the car is at a given rate of angular acceleration. It's in PSD mode because it gives a logarithmic scale and you can therefore see high frequency details better (but you can justify the power aspect by seeing the yaw as a physical result of physical inputs, much as you would for suspension movement and NVH).
The first thing to notice is the sudden drop off after around 4 Hz, we'll see in a moment that that drop off does not exist in the steering input - this here must be due to something else. Namely, the physical model of the car's rotational inertia. This is the reason for low-pass filtering down to 3 Hz for the acceleration (you can't get sharp cutoff without high order filters, and high order filters store energy and deposit it elsewhere in the system - lowering the cutoff allows for the knee to extend a touch past 4 Hz.) Anything above about 4 Hz is not a direct representation of the player's input, because there will be substantial stored energy in the inertial model. The inertial band can be seen to extend to about 15 Hz, with a few nodes and anti nodes along the way. The fact that it is the same shape for each lap is a good indication that the chassis and suspension setups are similar, and that the rotational moments are the same, on average.
The corners on this track last about 5 - 10 seconds. The combo of turns 2 and 3, taken together, add up to 5 seconds, but the steering is very subtle (steering via throttle and brakes, adjusting with the wheel) at that point. The region on the FFT corresponding to the corners, initiating yaw and then halting it again, would therefore be in the region of 0.1 to 0.2 Hz. Anything faster than that is, by definition, a correction or external influence.
It can clearly be seen that the oscillations in yaw rates between about 0.2Hz and 2 Hz is generally higher for 1.15, i.e. up to 7 dB (over double the amplitude). The same applies for the yaw acceleration. Beyond 2 Hz, 1.16 is higher, implying a snappier, more adjustable drive, up to the inertial band. Within the inertial band, the resonances are slightly more distributed in 1.16 (less peaky, more complex).
The noise floor is at about -95 dB power (~1/56000 amplitude), reached at 15 Hz - considered negligible.
3.
In the steering input, the story is much the same for steering angle as it was for yaw rate, less steering input at low corrective frequencies. The extra input at freqeuncies above about 4 Hz is obvious here, extending to about 10 Hz (a practical limit for player input). That clearly shows the player is interacting more with the inertial model directly, right at its sweet spot.
The story is different for steering rate, however, showing that lock is added on and removed considerably faster in 1.15 (peaking at 1 - 3 Hz) than in 1.16 (peaking at 0.4 - 1 Hz). This again points to stability and predictability.
There is significantly higher steering input at 0.1 - 0.2 Hz for 1.16, again implying less adjustment in the steering once committed.
4.
This shows steering input vs yaw rate in the left image. The correlation should be obvious and intuitive. Note that anything in the top left and bottom right is counter-steering. There is less of it for the 1.16 lap, the little loop in the top left in red is the split-mu event at turn 2. The top right and bottom left extremes are slow corners, and faster corners inhabit the vertical zone in the middle. That exemplifies the balancing role that steering has at high speeds, a wide range of steering inputs generate / sustain similar yaw rates.
The second image is showing the semi-equivalence of yaw rate and lateral force. For inertia consideration, we want yaw rate only. It should be clear the total grip hasn't changed. The almost vertical lines are fast corners, and the s-shaped lines are the slower corners. Again, this should be intuitive from the definition of lateral g force.
5.
This map shows steering angle over the track, 1.16 is the inner trace. The smoother input, especially at corner entry, is obvous.
6.
This map shows steering speed, 1.16 inner again. Red is adding lock (away from centre), blue is removing it (return to centre). It is intended to show the rate that the steering is being worked, and changes in direction / intent with the inputs also. Again, corner entries result in fewer changes in direction and slower steering speeds (less intense colours). Corner exits also have slower steering input, and more frequent corrections. Fast corners have much finer movement, at a much higher frequency, generally. The final corner has that characteristic "four-wheel-drift sawing" all the way around in 1.16.
All of this implies greater feedback of the car's attitude, in order that the controls are so much more precise.
The final two images, below as thumbnails, are only for interest.
The first, the yaw acceleration vs. steering angle, has its lines coloured according to steering speed (1.16 only). So you can see the two diagonals that adding (red) and removing (blue) lock form. The green vertical bars represent yaw contributions from inputs other than steering during hard cornering - slow cornering speeds further out at each side, faster speeds closer to the centre.
The last image shows the traction circle. Clearly, there is no extra grip, but the excursions in peak lateral load are slightly higher on occasion in 1.16 despite that. Also, more braking (vertical crossing lines) is performed at higher yaw rates, implying greater control and / or stability.
The only real conclusion is that the car was in better control in 1.16 vs. 1.15. The perception in-game is one of a better understanding of what the car body is doing, and the control inputs and resulting car behaviour above reflect that. It's possible this is the "MR fix" being rolled out to all other cars, whatever that fix was.
Motec's i2 is a wonderful piece of software, incidentally.