I think it will depend on who was writing, who was producing, and when the series was produced. The Klingons have served as stand-ins for China, which inspired their original appearance. In the 6th movie, they clearly meant to represent a post-Chernobyl USSR, though the strength of the analogy is questionable.
My theory is that when the Klingons were brought back for Deep Space Nine's 4th season, they were intended to represent the USA, whereas the Federation was now more analogous to the USSR. The Federation had largely eliminated class conflict, while the Klingons were still ruled by wealthy noble families. They Klingons couldn't take a shit without talking about how brave and honourable they were, but they snuck around in cloaked ships, and showed no hesitation in killing civilians. When the Cardassian fascist military government fell and was replaced by a democratic assembly, the Klingons immediately declared war on them. Feels pretty American to me.