I used to show a lot more remorse outwardly, because I wanted people to understand how sorry I was; now I think sometimes that just contributes to the drama, and sometimes they're not even the ones judging me or don't realize I did something, so I share if it makes sense and if it is important to the relationship; otherwise I just resolve to do better the next time.
I care about expressions of remorse only really as how it's applicable to the problem. If I don't trust sometimes intentions because they've never shown remorse, then yes, it helps to see the remorse until I'm aware it's there. But I don't much like people who bemoan a situation and go on about how sorry they are, while not resolving the problem. I'd rather they poured a lot of that energy into fixing the problem, once they 'fess up to their error. I don't need a lot of fancy talk, I just need a sense that, yes, they're sorry; and then we can move ahead.