R134A has different characteristics and operating pressures. I think you may end up with slightly less weight of refrigerant in the conversion which may reduce heat transfer capacity in a system designed for R12 (what your friend was referring to).. I have a 2000 so I haven't had to deal with the refrigerant issue on the NSX; but, I did have another 1987 vintage vehicle that went through the conversion around 2000. There might have been a slight impairment in the air conditioning system; but, it was not really obvious.
Doing the conversion is not dumb ass simple if you do it correctly. There is some tweakng to do on the final set up for optimum operation which a lot of shops may not bother with. Some details here:
R134a vs R12 refrigerant in the Porsche. R134a is a approved alternative refrigerant to replace R12 refrigerant in the Porsche.
griffiths.com
I have not been in a lot of NSXs; but, as a general observation, compared to other vehicles they do appear to be designed with excess AC capacity. If you put it on manual and max, mine can blow air that is cold enough to make your feet ache when it is 35 C outside. However, when I first got the car it was merely OK. While washing the car, I was alerted to a condenser problem by the stench of rehydrated dead grasshoppers. On checking, the condensers were about 30 - 40% plugged by dead bugs and a significant number of the remaining fins were squashed blocking air flow. After thoroughly wetting the grasshoppers to soften them I spent about 2 - 3 hours on my side using a fin comb to dig the grasshoppers out of the fins and straighten the bent fins. The low air entrance for the condensers make them extremely prone to accumulating junk. After the cleaning, I got a pair of Dali rock shields to prevent further accumulation on the fins. The shields are much easier to clean.
Check the condition of your condensers. If the fins are obstructed that will make it very hard for the system to reject heat to the outside when the ambient temperatures are high. Also, make sure that both condenser fans are operating and that the exit vents in the wheel wells are not obstructed. On a 1991, I would not be surprised if the fins are pretty banged up or one of the motors was dead. If the condensers are OK, take it to a good AC shop to make sure that the pressures are correct.