This is my first comment on the sub but I am aware of the rules and the high standards the mods set for the answers.

The 1897 war against the Ottomans is heavily criticized by historians as a nationalistic ill prepared attempt by populist groups in Greek society and military to assist their fellow Greeks in Crete that were fighting for their independence against the Ottomans. The results for Greece were catastrophic as she was forced to pay very high war indemnities to the Sultan in 1898.

These reparations were lend by the Great Powers and in order to secure that the loans would be payed back, an International Financial Control Commission (IFCC) was established in Athens.

But these catastrophic results shook Greek institutions deeply and eased the surface of new voices demanding reforms. Among these voices was Eleftherios Venizelos, one of the most important political figures in Greek modern history.

Venizelos though, had the assistance of a military movement, mainly of young officers, that demanded reforms in the Army, modernization of their equipment, meritocracy on the way army officers are promoted and restriction to the King's power to intervene in the Armed Forces. These demands were expressed with a military coup in 1911 that led to the election of Eleftherios Venizelos as prime minister.

As a prime minister, Venizelos implemented reforms in an unprecedented level. Most major reform was the new Constitution of 1911 and a spectrum of economic reforms in agriculture, taxation and international trade.

Diving to the core of your question, the most important changes in the Greek Army were the order of 100.000 Mannlicher–Schönauer rifles, several artillery pieces, ammunition and equipment for easier transfer of troops in case of mobilization. All the above mentioned reforms and military equipment purchases were tested in combat earlier than 1912-1913 Balkan Wars. The years from 1904 to 1912 saw Greece and Bulgaria competing in Turkish ruled (geographical-)Macedonia. So, to the North Greek volunteers joined the fight in Macedonia and at the same time in the South, Cretans were asking for their unification with mainland Greece. The North was a practice ground for young officers and their equipment and the South a diplomatic arena among Greece, Turkey and the Great Powers.

Lastly, a brief mention to what fueled these changes. Greek state, from 1830 until 1922 had big groups of Greek(-speaking) population in foreign states (mainly Turkey, Bulgaria and Russia). This fact mixed with the nationalistic ideas created a widespread belief that the Greek Kingdom of the 19th and early 20th century ought, in the sense of a duty to history, to liberate these populations by expanding its borders to include them within. It was called Megali Idea (Great Idea). And what in the 1897 war was a populist disruptive element in Greek society and army became an incentive for reforms in the years after it in the sense that Greece had to improve her infrastructure and army in order to pursue her national claims.

I highly recommend “A Concise History of Greece” By Richard Clogg (Cambridge University Press) and Gibbon’s biography of Eleftherios Venizelos.

While there were factors specific to Greece as /u/dimtriant points out, there were a couple other major factors worth noting, the big one being that while the 1897 war was indeed Ottomans vs Greeks, the 1912 war was Ottomans vs Greece, Bulgaria, Serbia and Montenegro. Most of the fighting was actually done by the Bulgarians, and Greece, while certainly important, was something of a junior partner.