Let us suppose that X is some utterance. It could be anything. For example: (1) X = Politicians are corrupt Now, if you say "One often hears that X", it means that it is uncommon that somebody you talk to is going to tell you X. We could go so far as to say that it expresses a common opinion. We can replace "One often hears that X" with "X is common opinion" and observe that there is no big change in meaning. Going back to (1), we have: One often hears that politicians are corrupt --> It is uncommon to hear somebody talk about the corruption of politicians --> That politicians are corrupt is common opinion. I hope it helps!

If you say "I often hear that", you're being more specific and talking about yourself I feel like these days when people are saying "One often hears", they're probably going to give you some sort of wisdom, or facts, or something along those lines. I'm no teacher, but hope that helps！