The United States Navy commissioned its newest destroyer, USS Zumwalt (DDG 1000), a few years ago. It's had a hiccup or two, but make no mistake, this is a very modern naval warship. It has tons of firepower, including two 155mm guns, 20 four-cell Mk 57 vertical-launch systems, and two 30mm guns. But how would it fare against the best surface combatant in the Russian Navy, the Pyotr Velikiy, the last of four Kirov-class battlecruisers?
This sort of ship-versus-ship combat looks one-sided in favor of the Russian ship. The Zumwalt is designed to hit and kill targets on land using BGM-109 Tomahawk cruise missiles and has some self-defense capability with the RIM-162 Evolved Sea Sparrow Missile. The Pyotr Velikiy, on the other hand, was primarily designed for naval anti-air combat, armed with SS-N-19 Shipwreck anti-ship missiles, SA-N-6 Grumble surface-to-air missiles, and a twin 130mm turret.
Looks can be deceiving. While firepower matters in any sort of combat, you need a target for that firepower. The Zumwalt, with its stealth technology, is a very elusive target. Yeah, one or two SS-N-19s could leave it a burning wreck, but they'd need to find it and hit it first. On the other hand, the Kirov's not that stealthy. Its radars might as well be a big signpost saying, "I'm over here!"
Furthermore, the Zumwalt has a few more anti-ship weapons options. One of which is Vulcano technology, which transforms its 155mm guns into anti-ship missile launchers. This places the Kirov in a world of hurt. Seeing as the Zumwalt can carry 300 rounds for each of its two 155mm guns, that's a lot of threatening firepower. Furthermore, some advanced versions of the Tomahawk missile can be used as anti-ship munitions. To make matters worse for the Pyotr Velikiy, the Zumwalt is likely able to be upgraded with systems like a ship-launched version of the LRASM.
In short, the real winner of this fight will come down to who can see the enemy ship first and in that department, the Zumwalt has the edge.