"Being nice" doesn't count, for example. There are plenty of nice non-Christians. One possible view is covered over at Inhabitatio Dei.
Christian distinctiveness | Inhabitatio Dei: "Here is the point of distinctiveness, according to the author: not that the Christian possesses an alternative cultural reality over against the ones in which they are set, but rather, that, regardless of their cultural setting, they manifest a distinctive character of involvement in it."
From that analysis (and you should really read the whole article), the distinctive is that we don't build cities as Christian cities. We don't build nations as Christian nations. Being Christian transcends the structures of humanity in the name of love (see the parable of the Samaritan, for example). Christians are marked by what we don't do, rather than what we do.
There seems to be something lacking from that, though - yes, I realise the irony of saying that in the face of a kenotic interpretation - and I can't help but feel that it's only the emptying without the action. Badiou's view on truth, expounded in his excellent analysis of Paul, relies on a distillation to a single, positive, axiomatic command. "You shall love..." It's not a prohibition, because prohibition instills the corresponding urge to commit that sin. Rather, it is the positive definition of what must be done.
Christianity, defined as absence alone, doesn't seem adequate to me. Absence of the world from the Christian, coupled by the presence of the command to love, is a fuller picture. Perhaps this is what is meant by, "they obey established laws, but transcend them by love (5:10)." And maybe that's the reason that it's so difficult to pin down precisely what it is that Christians do only because they are Christians.