Well, the Triple Alliance was made of very divergent countries with opposing, conflicting interests: Italy, Romania (which joined in secret), Germany and Austria-Hungary.
Italy wanted to colonize Tunisia and other parts of North Africa and create a colonial Empire. It also wanted Austria to give back the northern regions of Trentino and Istria which were Italian-populated. Being unable to colonize Tunisia, Italy seized Libya from The Ottoman Empire; this enraged the Austrians and the Germans, who had alliances with the Ottoman Empire. Italy left the treaty in 1915 and joined the Allied Powers.
Romania had issue with Austria Hungary, since Transylvania and other historically Romanian areas had been seized by Hungary and its ethnic Romanian inhabitants were being forcefully magyarized. Romania left the treaty in 1916 and also joined the Allied Powers.
The Triple Entente on the other hand, did not have such colonial or territorial conflicts. The British Empire had solved its colonial differences with France back in 1904 (mainly in Africa). The Russian Empire solved its colonial rivalry with the British Empire in Asia in 1907 (end of the Great Game). This allowed them to enter WWI with a more solid alliance. However, they did have political differences: France and Britain did not really feel close to the Autocratic Russian Empire but that subject tis not part of the question.
