Ori is more frequently used between two clauses, and sau between two words. That's what a native romanian tells me. So sau would be more idiomatic in the present sentence.
The difference is that barbatul is a masculine word, and femeia is a feminine word. -ul is not added to the feminine words. Barbat - barbatul. Femeie - femeia.
Why "the tea" is "ceaiul" while "the water" is only "apa"? Tea = ceai and the tea = ceaiul. And for water : water = apa and the water = apa too?? Is there a logic?