As others have pointed out, there are two different types of MO: the Ideologically Modern and the Behaviorally Modern.
The Ideologically MO have several main hashkafic differences with the Charaedim:
1) The MO believe in trying to fit the Torah together with the modern world and its culture, while the Chareadim believe in keeping away from any foreign culture as much as possible. This debate is the root cause of differences in how secular education, movies and TV, etc. are looked upon in the Modern and Chareadi worlds.
2) The MO usually hold a positive view of Zionism, while the Chareadim look at it as foreign and dangerous.
3) The MO have a much narrower view of the Mesorah than the Chareadim do. This gives the MO much more flexibility in deciding how to approach any situation. Also, this can arguably be called the root cause of all the other hashkafic differences that exist between the Chareadim and the MO.
4) The MO advocate giving women a larger and more public role in Judaism, while the Chareadim advocate a more traditional role for women.
5) The Chareidim often try to make sure that they follow every possible halachic opinion (chumros), which is not as common in the MO world.
The Behaviorally MO do not necessarily share any of these hashkafos. They are simply “modern” because they are not as traditional as the Chareidim. The Behaviorally MO are often far more lax with the Halacha than either the Chareidim or the Ideologically MO. They will often rely on the most lenient halachic opinion, and sometimes even (CH”V) ignore the Halacha altogether.