Game crashes constantly! Get it together GOG - no excuse for a 30 year old game taxing a PC.

Which one of the two?
Privateer 2 is inherently buggy, it's not a matter of being taxing. It's a matter that the game was basically a barely working alpha version put together because the publisher was fed up with the Roberts brothers' shit.
Try darkfix, that usually makes the game a bit more stable. Be warned though: it's still Privateer 2.

If it's the first Privateer there migth be something in the DosBox configuration that your PC doesn't like for some reason, in that case please post your configuration hardware and software. I never had any particular problem with the GOG version of the first Privateer so it might just be something weird.