We probably wouldn't have had as much technicologic inventions and the leader system would probably be messed up as well.
I believe Horace means that Greece won freedom from the Romans and somewhat ruled them. Like you said, Greek architecture, art and science merged with Roman knowledge. Furthermore, Greeks controlled the Roman Senate.
I think you're trying to see the "fight" from both sides. You can't. For this assignment, you have to write from the perspective of Greeks being victorious.