Well, it all depends.
If that particular military force was nothing but the personal police of a brutal dictator who used it only to protect his own power, I'd feel it was justified calling it a costume. Considering that members of this military had no problems executing their own and were controlled with drugs, I doubt it was a well disciplined force meant to protect a civilian populace.
I can't recall exactly which uniform Q was wearing when Picard said that, but I think it was the US or French uniform - not quite appropriate to call it a "costume", unlike the fictional 21st century soldier. Also an odd choice since Roddenberry had a military background. Was he ashamed of his wartime experience? Anytime the notion of military popped up in Trek, he got angry (Star Trek VI, in particular). Yet Starfleet mirrors the US Navy, but Roddenberry always said it was a peaceful organization. Eh, too much to wrap my head around. I prefer post-Roddenberry Trek anyway (ST 2-6, post S2 TNG, DS9). It dispenses with the "Mary Sue" humanity.