I'd have to watch the episode again to remind myself of the specifics, but it occurs to me that the Quad has a lot of different factions in it, and the military might prefer to see one of its ships destroyed than to leave it to fall into one of many sets of wrong hands.
Well, so was Kiera at the start. Heck, it took her over two and a half seasons to begin to question the morality of her system. Killjoys is clearly setting up a similar kind of arc, with numerous characters over the season urging the main characters to realize that sooner or later they'll have to take a side. And I think they did step up and take a side in the season finale.
Anyway, I'm not interested in pitting shows against each other. Building one thing up doesn't require tearing another thing down. Personally I think Dark Matter is the weaker of the two shows, but I want them both to succeed.
It's not clear to me if "the military" is part of the Quad. I suspect it's from outside the Quad; the (semi)military forces inside the Quad appear to be from the company or from the Rack. D'Avin had been in the military and outside of the Quad for years.
Kiera indeed was oblivious and brainwashed about her future and the corporate congress. However, both in flashback (from her POV) and in the present she showed ability to question moral values (like when she discovered 2077-Piron kept food back to increase prices, or in the present when she played into Liber8's hands deliberately by forcing a confession from that kidnapped corrupt CEO in S1).
Kiera was nearly always sympathetic on a week-to-week, case-by-case, decision-by-decision basis; the contrast with her eventual goal of restoring the bad future (for the first seasons) made Continuum a good show. The Killjoys, on the other hand, gleefully worked their warrants for the company, apart from not taking level 5 warrants. They seem harsh characters in a harsh world to me (the corporate future in Killjoys is even worse than in Continuum and Dark Matter, I think, the Company owns the Quad), until they finally start to see problems at the end of S1 when they begin to turn on the Rack and the Company.
The dichotomy between Kiera as a more or less sympathetic protagonist on the one hand, and the bad future she fought for on the other hand, was also an item in Continuum-discussions from the start. I have the impression this was far less the case with Killjoys, usually viewed as an enjoyable, flashy SF romp without many questions asked about the allegiances of its characters.
About Killjoys vs Dark Matter, I would like both to succeed, too. But the forums that discuss them seem to end up pitting one against the other, almost inavoidably. I am apparently in the minority, but I like DM's style of storytelling better and the characters interest me more.