I constantly see people online talking about the Tiger like was some kind of mystical battle unicorn that could tear swathes through shermans and come out with only some scratched paint. So let's take a look at it closer and see if it really could have deflected Shia Lebouff's marksmanship. (This is a long one, get comfy!)
So the Wehrmacht was doing pretty good with Panzer 3's (for killing tanks) and Panzer 4's (originally for infantry support) up until now. Many of the countries they invaded had little to no idea how to deal with the combined arms of the blitzkrieg and this negatively impacted high command's idea of what made tanks good. They believed no one could build a tank with more than 100mm of armor or field a gun much bigger than 75mm. Favoring tanks which could move fast enough to force the enemy into a surrender before heavy tanks could be useful, they took on the Soviet Union with these babies and hit an unwelcome surprise.
The Soviet Army had access to much better diesel engines and suspensions early on, which led to the development of the KV-1 heavy tank. It kicked ass everywhere it showed up, sporting thicker armor and a bigger gun than anything the German Army had at their disposal. Not only that, but T-34 production started to kick in, meaning there were lots of medium tanks supporting these beasts where once there were none. In a desperate attempt to drop these monsters from a safe range, the Wehrmacht soon learned their 88mm anti-aircraft guns had an incredible punch and with that the race to build a tank that could carry it was born...
but this is where Germany had a big problem. The fancy curved armor the Russians used to get more tank with less weight used a time consuming and expensive production method called casting, where the whole thing is made in one go, not just welded or bolted together like most tanks of the time. Germany needed to be able to make a lot of tanks fast if they were going to get back ahead of the Soviet Union in firepower. So they compromised. The Tiger was built with the finest materials they could muster and featured a fully welded hull and turret, allowing the most strength they could get without using casting. However anyone looking at the Tiger can see it's basically a huge box, and that lack of angling made it's armor basically useless. By the time it would see battle against Russia, the only tanks they would fight were T-34's and KV-1's, both of which had large caliber guns easily able to abuse this oversight.
So the Tiger gets built and right away they're sent to the eastern front. They cost twice as much as the panzer 4 and apart from having one of the best tank guns of the war, they're poopy. Crews struggled to learn how to drive them without overheating them or killing the transmission, tracks broke or wheels froze together, and they were too heavy to drive on bridges or through Russia's swampy plains. Meanwhile Hitler's side ho Krupp builds a kickass 75mm gun for the panzer 4 that makes it viable again, and they strap that thing on literally every tank chassis germany ever got a hold of (see panzer 4, stug 3g, hetzer, Jgdpz 4).
This is one of those moments in World War 2 where if you sit back and really think about what happened, you find it hard to believe that brutality on this scale could have even been dreamt of in a work of fiction let alone be allowed to happen in real life. With the new Panzer 5 medium tanks, Germany collects all it's armored might in an attempt to encircle a protruding element of Russia's forces. Thousands died on both sides and in a field of chaos where the Tiger was able to reap from the back lines, only here did they shine. Germany would go on to lose their ability to take the offensive for good on the eastern front, and over 100 tigers (nearly 10% of all tiger 1's ever built) were lost or abandoned. The remaining Tigers would spend the rest of the war in a slow retreat trying to fend off an unending horde of T-34's.
The Sherman's had armor adequate for the tanks they encountered (60mm sloped at 40 deg. full cast construction with welding) and statistically were one of the most successful tanks of the war. Only 3 times did the Western Allies actually fight Tiger 1's. First time: Shermans shot the Tiger a bunch and it died. Second time: Tiger blew up a Pershing (Pershing sucked too), and then the Shermans killed it. Third time: Tiger was being loaded onto a train and couldn't fight. It died. Point is 1) Most Tigers were gone by the time we showed up and 2) if the Tiger 1 was less than 2km away from a Sherman, the Sherman just had to shoot it in the hull and it would die 90% of the time.
Tiger 1 production stopped before we even hit Normandy. So what should've been trading blows with Wardaddy is this monster: the Panzer 6B king tiger (or Tiger 2). Germany had mastered welding flat armor plates by now and they had much stronger engines like the Maybach HL240. Taking everything the Tiger 1 did wrong and processing it into this behemoth, they now had a platform which could carry the 88mm gun and be immune to enemy fire from in front. Although it doesn't take a history buff to know that it was too little too late at this point, and the 500ish tiger 2's they made had little impact on the war as a whole. "Fury", up until the Tiger scene, was one of the most acceptable portrayals of life in a Sherman and simply swapping the iconic Tiger 1 for a more historically accurate Tiger 2 would've made the movie more satisfying to this tank nut. If you want to learn more about some myths of Allied and Axis armor, take a peek at https://www.youtube.com/watch?v=bNjp_4jY8pY . The guy does a lot of source material research to find out about this stuff, and it's well worth the listen if you like this kind of thing.