How a nineteenth-century cruiser fares against WWII escorts

Could a nineteenth-century cruiser defeat a WWII destroyer, frigate, or sloop in a one-on-one fight?

A WWII destroyer is favored because of its torpedoes, while frigates and sloops have less certain advantages and may need to close dangerously.

A WWII destroyer differs from the frigate and sloop alternatives because it carries a credible torpedo threat. The smaller escorts have modern fire control and depth charges, but using the latter against a surface ship would require a dangerously close approach. A nineteenth-century cruiser therefore does not become harmless merely because its opponent is newer. The comparison is useful for seeing how weapon type, engagement range, and fire control matter more than a simple difference in date.