What military strength made the Athenians the most powerful city-state in the Delian League?

The military strength that made Athens unquestionably the strongest city-state in the Delian League was its navy. The Delian league was formed to fight the Persians, who were a seafaring enemy with their own navy. The Greek city-states most vulnerable to Persian invasion at that time were islands on the Aegean Sea and also on the Anatolian Peninsula (aka Asia Minor), and they sought protection from the Persians with the assistance of the Athenian navy. With so many city-states seeking its protection via its navy, Athens was able to gain more power and influence politically in the Delian League and was clearly its most prominent member. Therefore it can be said that Athens' navy not only gave it its greatest military strength, but also allowed for Athens to have great political power and influence as well.
Many would erroneously believe that the Spartans would have been the strongest member in the league; however, Sparta was landlocked and had no navy whatsoever. Their strength was their infantry, which could only fight on land. In this particular war, a navy was more important since the enemy was arriving by sea. A navy also allowed Athens to move its troops where they needed to go and to launch amphibious assaults.
One of the most famous examples of the strength of the Athenian navy was the Battle of Salamis. In this naval conflict, the Persians lost about a third of their navy, causing Xerxes to call for a retreat (Lendering).
https://www.brown.edu/Departments/Joukowsky_Institute/courses/greekpast/4773.html