We know that Klingons have the technical ability and know-how to modify the cloak. In Star Trek VI, they have a bird of prey that can fire weapons while cloaked, a no-no even up to the Voyager era (the idea being that the cloak requires much of the power of the ship, and any weapons system will emit signals that must be cloaked as well). They also know how to discard modifications that don't work out for their tactics.
The Romulan-Klingon Alliance was responsible for Klingons getting the cloak. They didn't develop it themselves; during the short lived alliance, Klingons traded D7 cruiser technology for cloaking technology. After the alliance dissolved, their technology would diverge.
In fact, a technology divergence would be tactically necessary! As opposing empires, having a common cloaking technology would be bad, as they would know how to build countermeasures for each other.
We also know for a fact that Klingon cloak is different than Romulan cloak... and that Klingon cloaking devices have been advanced over time. In Star Trek: Generations a Klingon D-12 Bird of Prey has it's cloaking device triggered by an ionic pulse; that model of cloak was retired because of this weakness. However, this "trick" is never used on any Romulan ship, and it's never brought up as a possibility against any other Klingon cloak.
So, we can say for sure that Klingon and Romulan devices are different. There's no indication that Romulan cloaks are SUPERIOR, but that they ARE different.