Hard to compare when not comparing like with like but I can confirm that steering feel is more precise on the bikes I have with 31,8 bars (road bike, cross bike and Pace 303) And "flex" feel under load is a lot less noticeable on these bikes than it is on my classic bikes.
The road and cross bikes have both had similar quality 25,4 bars fitted previously and steering feel was greatly improved by change to 31,8 (which I resisted for 2 years till finally accepting progress).
If you are running modern forks with very little sideways flex, then the weak link would be a bad choice of handlebar, and you will notice it.
If there is flex in wheels or forks, then you are less likely to.
Completed: 94 Stumpjumper w. M733; ; 92 Dave Yates 731 ; 97 Parkpre Pro-Elite ; Pace RC200 F6 ; Pace RC300; 82 Gios Super Record ; 97-8 De Rosa Giro D´Italia; ; Banani SPX Track bike ; 89 Alan/Mavic Cross Bike ; 05 Focus Cross Team ; 90 Look MI-80 all-Mavic ; 12 Focus Izalco Team/custom build ; 11 Focus Thunder Custom build
Projects : , Brouwer all-Mavic
Stripped : Pace RC303
Gone : GT Karakoram
Stayed in the family: Kuota Kharma, 04 Stumpjumper FSR
Ceased to be : Dynatech MT3, killed by corroded seatstays.