Depends - if one vessel decided it would be worth investigating the other one, then something might happen. At some point, the two ships would figure out both vessels were pirate vessels. Pirates seemed to not want to fight each other - they were both doing the same thing and pursuing the same goals. Pirates who met might even talk and decide to work together as sea, aka work in consort. The other side of the issue is that a pirate vessel is a vessel that is often well armed and crewed with many men - attacking it is high risk and could result in casualties. Pirates were very selective about what they would risk attacking, which is why they mostly attacked merchant vessels. Merchant vessels didn't necessarily have huge crews of fighting men (some did, but plenty had just enough men to sail them, crew cost money after all). The only time I remember two pirate crews really being combative towards each other was in 1719 on the coast of Sierra Leone when there were some disputes between two pirate crews out of three crews present - but the pirates did avert an all-out fight.
Is there even such a thing as a "Golden Age of Piracy"?