It is difficult to declare a definitive winner, as the outcome depends on training, experience, and physical condition. However, we can compare the general traits of each group:
Spartans
Strengths: Rigorous training, discipline, and skill in hand-to-hand combat, archery, and javelin throwing. They were well-equipped with armor, the hoplon shield, and the doru spear.
Weaknesses: Less mobile than some warriors and sometimes inflexible in tactics, making them vulnerable to surprise attacks.
Barbarians
Strengths: Ferocity, physical strength, larger size on average, and skill with swords, axes, and spears. Many were also capable horsemen.
Weaknesses: Less formal training and discipline, and a tendency toward overconfidence that could lead to mistakes in battle.
Overall, Spartans likely held an edge in training and discipline, while barbarians likely had advantages in size and raw strength.