Really, the seeds for the Klingons displacing the Romulans were planted back in season 1 of TOS, when the Klingons were created for "Errand of Mercy" to displace the more makeup-expensive Romulans. The Romulans were only used in one more significant appearance in TOS, whereas the Klingons became the Federation's main foe.
Then in TMP the Klingons got their makeover. We didn't get much of look into their culture or attitudes in that brief appearance, but surely the new look informed how the Klingons were treated afterwards...from that point on, they demanded to be more than scheming moustache-twirlers...and they demanded to be used more than the Romulans, who were pretty much stuck looking just like Vulcans.
We can thank TNG for bringing the Romulans out of mothballs at all, however they chose to portray them. And that was only after the major misfire of trying to set up the Ferengi as a worthy adversary.
Over the course of Trek history, the Romulans simply got a heck of a lot less development. They became known for being manipulative pretty much by default, to differentiate them from the TNG-era Klingons. The one capsule description of the Romulans that sticks out to me is when Picard says "It's always a game of chess with the Romulans." Really, this could describe the TOS Romulans in "Balance of Terror" as well. One thing that is often overlooked is that the sub-commander in that episode was being portrayed as an individual who didn't agree with what his people wanted him to do.