For me they've always sounded identical to how the AR2 and RPG sounded when held by the player and even with the weapon sounds mod that's compatible with MTB's animation pack (thank you btw) even with that they still sounded the same as when held by the player, heck even Garry's Mod it was the same there too.

Not an issue. Base game; they have separated sound effects in their respective directories
apc_mg_fire.wav and stinger_fire1.wav
I couldn't find a proper replacement for the APC so I made it use the same sound as the AR2
This will only be an issue if you have a script that makes them use different sound files

Then that poses an issue, because on my end the APC uses the same sounds as the AR2 and RPG which will result in a conflict with the weapon sounds.

It changes the APC's mounted pulse gun & rocket launcher sound effects. There is a preview near the end of one of the showcase videos in the main addon

Ok, when it says that it includes the APC, does that just mean when its in motion? Because unless I'm mistaken the rockets and gun on the APC use the same sounds as the AR2 and RPG.