Always Save The Girl / Loved I Not Honor More: Well, as a matter of principle, the Imperials prefer to Take a Third Option whenever possible, by way of giving the finger to the sort of people and/or fates and chances who like to set up this sort of Sadistic Choice.
That said, given their views on Honor Before Reason, they do tend to go with the Loved I Not Honor More side if they can’t find a third option, if only because (and remember, this is a gender-neutral pair of tropes in this setting) they know perfectly well what the loved one in question would have to say on the issue. When, you understand, it is a matter of principle.
Subverted, however, exceptionally brutally when the people responsible for this choice haven’t quite grasped the nuances of the Imperial value-set (see: Blue and Orange Morality, et. seq.) they’re counting on to save their asses; those, for example, who think that John Q. Imperial won’t go for Always Save The Girl because they’re hiding behind their own population or within a cooperative/non-uncooperative population and the collateral damage would be too high are likely to very rapidly learn that the body count of people even merely passively sympathetic to this sort of thing ranks somewhere below cost of ammunition expended in his decision hierarchy.