One of the major differences is how to handle the modern world. Both MO and chareidi Jews agree that the world is filled with things that are dangerous to a frum Jew. Let’s take the internet as an example.
MO says, “Yes, the internet is dangerous, but we recognize that we can’t block it out. Therefore, let’s educate ourselves and our children about it, and show them how beautiful the proper path is. Therefore, when the temptation arises (as we know it will), we will be better equipped to withstand it.”
Chareidi Judaism says, “The internet is dangerous. Therefore, let’s assur it. If our children can’t access it, they won’t have to face the temptation.”