I would say that the dynamics shifted, rather than one becoming the other. If you follow the Rihannsu books, you can see a pattern of ambition, expediency, self-serving politicos, and political backstabbing creeping its way into the Star Empire and crowding out the old school officers and enlisteds who were brought up with the honor code of Mnhei'sahe. Crowding them out as dangerous to the ambitions of those who wanted power. In some respects, it was even pushed along by the rapprochement between the Federation and the Klingon Empire, making many ambitious young Rihann feel that their homeland was becoming marginalized, not to mention the idea these fellows got that once the Federation and the Klingons were allied rather than merely not fighting, they would soon turn their attentions toward the Star Empire. And so the Star Empire becomes another China, pre-Nixon, while the USSR that had been the Khomerex(trans: (n) Structure that grows. ant. is khesterex literally meaning "structure that dies") Klin became analogs to the honorable Russians of which people like Vladimir Putin make you question the existence. And certainly even the Honorable Klingons had their share of people whose ambition outstripped their ability to the point of forfeiture of honor (The House of Duras, anyone?) or whose paranoia about potential rivals did the same (e.g. Chancelor Gowron). Yet even in the worst days of the Klingon Empire losing its way, there were still honorable officers in its ranks. Qor, Qang, and QolotH, known more commonly to the Federation officers with whom they tangled as Kor, Kang, and Koloth, are but three of the better known. In our own continuity here, we have Kahd, Dath'mar, and others still.
So, continuing the parallels to 20th century Earth, you have the Klingons as Russians, first in Czarist version as we met them during the events surrounding the Earth Command Starfleet ship NX-01 Enterprise, then at some point between then and when we first meet them in Kirk's day, they've had their Krazny Oktyabr, and have become the USSR of the 23rd Century, but honor still remains with many of them. Late 23rd Century they start finding the old ways again, while the Rihannsu start to find their way ever more rapidly towards the backstabbing dishonorable sneaks we know and loathe. The old guard of the more Soviet minded types of the Klingon empire are scared of losing their position and power. They conspire with the emerging ambition-before-everything-else Romulans and with some Old Guard Feds who are also scared of change in a last ditch effort to go back to the status quo. This is foiled and friendship is slowly forged between what most had thought were implacable enemies, just as the Organians foretold. Thus the pattern is set for the 24th Century at least up until the Nemesis incident.
Of course, I have to admit to constructing a lot of this timeline myself based on material that, while not considered technically canon, has yet to be contradicted on screen. YMMV.