Yamato...
Her armor is superior in all areas, although German steel is superior to the IJN variety of the time. You also have to look at the design doctrine of each ship...
Yamato was built to outclass American ships by brute force - bigger guns, more armor. The Bismarck and Tirpitz were designed for North Atlantic, and North Sea, close-quarters, flat trajectory gun duels, similar to what the Germans encountered at Jutland...remember, Jutland was a major factor in German ship design in the years that followed. Her armor scheme reflects this, with an armor layout that makes it difficult to put a shell into her vitals at short range, but which is vulnerable to long-range fire, and which reduces the total amount of protected volume in the vessel by carrying her armor deck lower in the ship than her contemporaries. Bismarck and Tirpitz also suffer from very shallow armor belts, which do not extend to the undersides of curvature of the hull, which is why Bismarck suffered severe damage from Prince of Wales 14" guns. This was never addressed with Tirpitz.
With regards to optics, both the Germans and Japanese had very good optics, but again, after 1943, radar gunnery had rendered optical sighting obsolete. In the case of both the German gunnery radar (Fumo 23, and the Japanese Type 2, Mod 2), both lacked training capabilities. Radar operating at meter or decimeter wavelengths is useful for ranging, but lacks the angular accuracy necessary for training. In practical terms, this means that a decimetric set can develop a range solution via radar, but must rely on an optical director to supply training information for the battery. This hybrid fire-control solution is, of course, limited by the quality of the optics available, and also by the visual horizon (which is closer than the radar horizon), and weather conditions. Only with the advent of 10cm and (later) 3cm wavelength sets was true 'blindfire' radar fire-control achievable, wherein the firing ship need never come into visual range of the opposing vessel. The Germans, Japanese, and Italians never developed sets of this capability. Both the Japanese (despite its 10cm wavelength) and German sets were usable for fire control against a battleship-sized target only out to a range of about 27,000 yards, which is close quarters for battleships.
So at long range, no one really hits much of anything...but Tirpitz would fair worse than Yamato if she were hit. At medium range, Yamato's plunging fire will decimate Tirpitz 4.7 inches of deck armor, while her 15" will have more difficulty in penetrating Yamato's 9.1 inches of steel. Again, at close range, Yamato clearly carries the advantage in armor, and her sheer weight of fire would pound Tirpitz.
At short range, Tirpitz carries a speed advantage of 3 knots, and her damage control is probably surperior, however, more damage control will be required when hit with an 18" shell, and the IJN Type 91 shells that fell short were designed to travel through the water and impact the side of the target, which would be devastating for Tirpitz and her shallow armor belt.
When you consider the designs of both ships, Bismarck and Tirpitz were designed to outclass the King George V Class of battleships. Yamato was designed to outclass anything the US could possibly dream up. The notion that the Yamato was designed to better the Iowa, or vice versa, is wrong. Both ships were being designed concurrently, and the tight security around both insured that no one was playing catch up to the other.
At any rate, I digress...
Yamato wins.
Jeff