Just wondering since you hear a lot about the Tiger I and it's fear factor it had, but the Tiger II, a much more daunting tank, isn't talked about nearly as much.
The first battle of King Tiger tanks was against British forces in France, on July 18th, 1944. Three King Tiger tanks were lost in this fight, including one that was stuck in a bomb crater, but it doesn't seem like the British took particular note of the new tank. A little while later, the Soviets encountered this tank on the Eastern Front, at the Sandomierz Foothold. King Tiger tanks were first used in combat here on August 11th. The Soviet forces also did not initially notice that they were fighting new tanks, mistaking the enemy for Panthers. The mistake was discovered only after the battle, when one of the tanks that the Germans abandoned intact was inspected, and a full set of documentation was found.
It would appear that the Americans were the last to discover anything at all about this tank. On October 4th, Major General John R. Deane wrote to the Soviet GABTU, asking about information on the "Tiger Imperial". Since full trials of the captured tanks were not yet performed, little useful information was returned, if any. The American 1st Army captured a functional tank at Duren, which yielded some information, at least the basic measurements of the tank, such as weight and top speed.
The British had some trouble with finding a tank for trials, even though they had a chance to get one first. Finally, on September 20th, they found a so called "Porsche" turreted King Tiger (in reality, Porsche had nothing to do with the turret, but it's a common mistake) at Plessis that could be examined. Unfortunately, all they had was the turret, but that allowed them to make some conclusions about the tank. The armour quality was poor, and there were sections on the front of the turret vulnerable to even relatively low caliber guns, such as the 2-pounder mounting the Littlejohn Adaptor, 75 mm gun firing HEAT, and 6-pounder firing APDS. An interesting feature of the turret that was noted by the examination commission was the interlocking of plates. This solution was deemed too complicated and time consuming to implement in British production.
By the time the report was completed, the British found out that this type of turret was a minority. Another type of turret was captured at Beauvais, but this time it came with the whole tank. The tank was not in running order, but the hull could be inspected. The conclusions were not radically different from those drawn before: German armour was still considered poor in quality, and the tank shared some weaknesses of the Panther and Tiger, namely that the sponsons could be knocked out by HE rounds that hit above the tracks, which would almost certainly trigger an ammunition fire. The quality of the welding was also poor. However, the King Tiger got rid of one of the weaknesses of the Panther, namely the ease with which one could ricochet shells off the gun mantlet and into the roof of the driver's compartment. However, the new gun mantlet offered poor protection from splash from the right side at certain depression angles. The upper front plate was also found to be invulnerable to British weapons, but the front and sides of the turret presented a more tempting target anyway.
On the inside, the tank showed more weaknesses. The crew positions were uncomfortable, with mechanisms placed poorly. The loader and gunner fared especially badly. A loader taller than 5'4" hit his head on the hatch handle, a loader shorter than that would be unable to reach some of the ammunition in the ready racks. Due to the heavy and awkward ammunition, as well as bad design of the breech guard rail, the loading process was slow. The gunner sat in an awkward position, had issues operating the flywheels or power traverse pedals, and had nothing to look into other than the gun sight, which meant that target acquisition was tedious.
Unlike the British, the Americans did take steps in response to the appearance of the new German tank. The HVAP T30E16 round, introduced for the M3 90 mm gun, was specifically designed for handling tough armour of the "big cats". The manual for that type of ammunition specifically mentions that it can penetrate even the upper front plate or the gun mantlet of the King Tiger.
Even though the Soviets were the first of the Allies to receive a working tank, a complete report was only available in February of 1945. Even then, the trials were brief, as the tank broke down constantly, and spare parts were unavailable. Trials showed that, even in the best of times, the performance of the tank was far less than what its manual claimed that it was capable of. The report concludes that the tank's running gear and drivetrain were very fragile and unreliable. The gun, on the other hand, was deemed good, but the semiautomatic mechanism broke down after 58 shots.
Firing on the tank showed that Soviet guns were more than capable of dealing with it. Even nonpenetrating impacts from 122 and 152 mm shells against the front armour resulted in cracking and spalling that would disable the tank. Like the British, Soviet trials concluded that the armour quality was poor.
Sources:
W. Schneider. Tigers in Combat. Vol.1 – Stackpole Books, 2004
Armour Branch Report on Armour Quality & Vulnerability of «Tiger» II Turret
Armour Branch Report on Armour Quality & Vulnerability of Royal Tiger
Armor Piercing Ammunition for Gun, 90-mm, M3
BIOS Final Report No. 614 Item No. 18 Welding Design & Fabrication of German Tank Hulls and Turrets