This is directly from the press kit. I personally do not mind any of the sounds and most people that are in the car comment how great it sounds inside the cabin.
"Intake Sound Control
To enhance the driver's visceral experience inside the NSX cabin, the Integrated Dynamics System can be used to engage the new intake sound control and active exhaust valve systems to fine-tune cabin sound quality and volume to match the selected dynamic mode. The sound pressure level range within the cabin between wide open throttle in Track mode and electric vehicle cruising in Quiet mode is 25 (dB)—a wide range of audible sensation.
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Active Exhaust Valve
The NSX active exhaust valve system is a complimentary component of the Integrated Dynamics system, offering quiet and refined driving or pulse-quickening sound at the will of the driver. Two electrically-operated valves are either open or closed based on driver throttle inputs and the selected mode of the Integrated Dynamics System
In Quiet mode, the exhaust valves are closed, and the exhaust gases are routed through silencers and out the two outboard exhaust pipes for a more subdued exhaust sound, allowing the driver to experience the intake soundtrack more clearly. Power and torque from the Sport Hybrid SH-AWD power unit is more than sufficient to effortlessly meet driver demands.
In Sport mode, the exhaust valves are initially closed. They will open depending on how aggressively the driver accelerates.
In Sport+ and Track modes, the exhaust valves are open, enabling maximum exhaust gas velocity out of all four exhaust pipes. This produces maximum engine performance and a full‑throated exhaust note.
The active exhaust valve system—together with the cabin sound modulation technologies of Active Sound Control and Intake Sound Control—serves to create a customizable auditory experience both in and outside of the NSX. From the hushed silence of Quiet mode to the full concerto of Track mode, the cabin fills with sounds every driving enthusiast loves to hear: the high‑performance "pop" from the exhaust when executing an upshift, the quick blip of the throttle upon downshifting and the occasional distinctive off-throttle burble that is a welcome reminder of the power and torque capability of the twin-turbocharged V6 engine."
In regards to the stop/start at stoplights and low speeds, I do not mind this system at all. It kicks in much smoother than any other vehicle I have been in thanks to the active engine mounts. Also, if you do not like this system you can switch the dynamic mode or you can push the drive button a second time to enter manual paddle shift mode. In manual mode the engine will never shut off even if you are in regular sport mode.
The ride is incredibly comfortable. My girlfriend has slept in the passenger seat for hours on some of the longer trips and she was plenty comfortable. That's saying a lot since the roads in Minnesota are definitely not the smoothest.