If a child is born to a non-EU member father and an EU-member (egPolish) mother outside of the EU - say in the country of the father's residence - does that child qualify for the same passport as the mother?
A child born to a Polish citizen outside of Poland is automatically a Polish citizen.
Polish citizenship qualifies the child for a Polish passport. There is no specific EU passport. Each member country's passport is evidence of EU 'citizenship' and all of those rights and responsibilities.