The Klingons never seem to view the Romulans or Cardassians as a threat to their empire. They are enemies for sure, but the Klingons never seem to present them as the threat the Federation was during their "Cold War" era days.
The Dominion is a threat and the Klingons react to it in ways similar to how they reacted to the Federation, but this time the Federation is there with them to try to keep them pointed at the Dominion. Remember that the Dominion was not even known to exist by the Klingon Empire until 2370 (when everyone else on the Bajoran side the Wormhole found out). That's nearly 80 years after Praxis exploded.
The Dominion is a threat and the Klingons react to it in ways similar to how they reacted to the Federation, but this time the Federation is there with them to try to keep them pointed at the Dominion. Remember that the Dominion was not even known to exist by the Klingon Empire until 2370 (when everyone else on the Bajoran side the Wormhole found out). That's nearly 80 years after Praxis exploded.