You said spanish favored object pronouns are preferred. So you wouldn't say ,mi radio se rompió you would say se me rompió la radio?
Although both options are grammatically correct, most natives would probably be spontaneously inclined to use the second one ("se me rompió"). Like with the use of the personal pronouns (yo, tú,...), possessives are used to make contrasts, so I'd use the first sentence in a situation like this:
Tu radio aún funciona, pero mi radio se rompió.
Here, I'm establishing a contrast between "your" radio and "mi" radio, so it sounds perfectly natural. However, without this contrast, it strikes a little bit if you say "mi" without any justification. It is like "What so much emphasis on YOUR radio, if you are the only involved in the whole scene'". Funny enough, if I said:
Tu radio aún funciona, pero se me rompió la radio. (''')
It would sound even weird too, because I start talking about you, then I say "but...", and when I am about to provide the other side of the story... (i.e. the contrast), I just talk about myself, ignoring YOUR radio altogether. Here, "mi radio" would be almost necessary.