Just as the Federation upgraded the Constitution design the Klingons upgraded their own cruiser, the D7 Battlecruiser. The end result--the K'T'inga Battlecruiser--was just as much a match for the improved Constitution-class vessels as their respective predecessors had been. Nearly evenly matched in firepower, gunnery, and damage potential, the two designs were the best of their period.
Soon after they entered service the K'T'inga received cloaking devices, a result of the brief alliance with the Romulan Star Empire. Newly developed and testbedded on other hulls, the Klingon Empire saw virtue in the ability to launch sneak attacks and then disappear. Despite the advantages of cloaking technology, however, the K'T'inga Battlecruiser was not a big enough leap in technology to make it superior to the Federation's Excelsior Cruiser.
After the Excelsior entered frequent Federation service, the age of the K'T'inga came to a close. The design was ill equipped to fight this newer Federation threat without superiority in numbers, and even then they faired poorly.
Ships of this class continue to be used in the Klingon navy, though they usually are acting in a destroyer role, escorting the larger Vor'cha Attack Cruisers or providing fire support for smaller B'rel Birds of Prey.