I have had both experiences. For me, it really depends on the other person because I'm very easy going. I have two exs that could not handle continuing a friendship after the relationship was over. I have an ex that I'm very good friends with and my ex wife and I interact regularly because we have children together. In my opinion, unless the other person was terrible to you, I don't see a reason to cut someone out. It can be hard to set the other stuff aside and just be friends. No one is going to know you better than someone like that.