TLDR: I don't buy the argument that saving Jaxo is the correct 'military' choice because it's based on making stuff up about the prisoners and exaggerating the effect a single SpecOps soldier might have on the war as a whole compared with the prisoners. Picking Jaxo is about making an emotional/personal decision to favor your comrade/friend/lover/whatever over your duty (It's not what I did in game but I definitely sympathize with it, and while I probably wouldn't have chosen her even if I were actually in that situation, it would have scarred me quite a bit).
Spoiler tags since other people are, I guess (although it's a spoiler topic so...)
As for the actual decision...
I was somewhat bothered by the choice when it first came up, but the begging to leave the other prisoners behind soured me pretty quickly (I can't imagine any of the squad doing the same), and I guess I lack the extra emotional oomph of having her sleep with my trooper since I was playing a female trooper. I felt bad, for sure (and recommended her for a medal, while not mentioning how she was acting at the end), but it was an emotional gutpunch rather than a particularly difficult decision.