When, to what extent, and how did their engagements turn out?
Assumption: Talking about 1690-1725 pirates in the Atlantic World.
Depends on who was calling who a pirate. You'll want to look into the Spanish Guardas De Las Costas for one of the biggest sources of what could be considered Spanish pirates taking British ships. Sailing under the guise of enforcing Spanish law in what was allowed to be traded with the Spanish, these vessels took tons of British (and other) vessels and justified their actions that the vessel had been illegally trading with the Spanish on the slightest pretense, even as far as the presence of Spanish money. But, the government worked with them, and took their prizes into Spanish ports (in particular on Cuba).
As for the kind of pirates that were "enemies of man kind" and didn't work with one of the European powers, not really many of those. The strong majority of those kinds of pirates were from Britain. Marcus Rediker in his book Villains of All Nations found about 700-some pirates that sailed in the 1710s and 1720s and their origins and found this, Spaniards barely show up among them.