First, we need to debunk an assumption from the get go: that is, the assumption that tanks exist to fight tanks. That's true now - vehicles like Abrams and the new Russian Armata were designed with destroying the enemy's tanks in mind. However, in WWII, this is not the case. The US Field Manual 17-10 sets out the duties of the Armored Force in American doctrine:

1.Role The role of the armored force and its components is the conduct of highly mobile ground warfare, primarily offensive in character, by self-sustaining units of great power and mobility.

There's nothing there about destroying enemy tanks. This is because that's not the primary role of tanks in the Allied armies in WWII: tanks that are fighting the enemy tanks are tanks that aren't doing the much more useful job of beasting into the enemy's rear areas and conducting maneuvre warfare. That's not to say they aren't meant to engage enemy armor, as is sometimes claimed - nowhere in FM 17-10 does it say that – but it isn't their primary role. This is a similar situation to the Soviets, where medium tanks are to conduct "deep operations" and heavier ones to create breakthroughs, and the British, who divide their tanks into "cruiser tanks" to exploit breakthroughs, and "infantry tanks" which are to support the infantry in creating those breakthroughs. A lot's been made of that, but in practice it was effectively just a distinction between light-medium and heavy tanks. The job of engaging enemy tanks was to be performed by infantry with attached anti-tank guns, artillery, mines, and tank destroyers. The US in particular is very fond of the tank destroyer concept, and although it leads nowhere, US TD units are very effective in combat, even though they were often used as regular tanks or artillery.

So – what does this tell us: most importantly, it tells us that the designers of Allied tanks were never really interested in playing the late-war German game of thick armor and giant guns. Indeed, neither were the Germans, in the beginning: the superficially impressive German designs of the late war were the result of ever-increasing requirements, brought on by their 1941 "tank panic" when they encountered the T-34 and KV-1. So whilst the Germans are designing "the ultimate driving machine" from 1942, the Allies are confident in their doctrine and their dedicated anti-tank units. When you assess the quality of a weapon system, you basically have to ask three questions:

What doctrinal niche or role was this system supposed to fill? Did it fill that role effectively?
Was it the most efficient way to do so?

So – we know what the Allies want from their tanks: fast, vehicles to exploit breakthroughs and conduct maneuvre warfare. What do the Germans want? Initially, the same thing, but later on when they feel that they need a new vehicle, Hitler and others pour new requirements into the design process – and the result is that the Panther's weight increases by ten tonnes.

So how do these vehicles do in practice?

Well, what we find is that the infamous "Big Cats" are total failures at the offensive operations that tanks are for.

The Tiger and King Tiger tend to have quite good availability rates, but that's because they have huge dedicated logistical tails, which makes them quite vulnerable to breakdown when they get ahead of them. That hampers them badly – especially as they break down often and are hard to repair.

The Panther is a whole other useless kettle of fish: I'd advise you to read the French report, summarized here, if you can find it. In essence, the Panther had a number of critical design flaws – no unity sight for the gunner and inadequate final drives – that meant it was effectively railbound.

By contrast, Allied tanks, whilst not necessarily having the biggest guns or the thickest armor, were quite adequate for the tasks for which they were designed for.

This answer is already too long, so I'm not going to able to detail other issues: firstly, that the German assessments of their own kills/losses are sometimes so exaggerated as to be essentially fraudulent. Secondly, despite the reputation that the "Big Cats" have in American culture, it was the British who did most of the anti-tank fighting in Normandy. And finally thirdly, the Soviet crews of the Shermans provided to the USSR through Lend-Lease seemed to love it – see Dmitry Loza's memoirs.

Also: the whole "5 Shermans vs 1 German tank" is bullshit.

The error is to assume WW2 as one moment. The war took multible years and tanks were changed and improved over time. No one nation, or one tank had better tanks all the time.

German generally did not have the best tanks, and they were outclassed in France and in the USSR. The answer to these problems came with the design of the Panther and the Tiger. These were better, in some ways, then soviet and other allied tanks. But the price of this early release was that the still had many problems, specially mechanically.

The allied then of course tried to answer these devlopment with there own tanks. The British improved on the M4 Sherman, and gave it a better main gun, called Sherman Firefly. The american produced the M26 Pershing that saw combate later in the war. Towards the end of the war new designs were ariving that saw little combate but were techically better then anything the germans could produce. See for example the British Centurion. The Soviets answer was a update to their workhorse T-34, calling it T-34-85. These were not quite as good as the Panther but was effective enougth to defeat Panther and Tigers in battle.

In the end comparing tanks 1 vs 1 is not really all that useful. The question of how they were used, or intend to be used is very importent. Maybe even more importent is how easy and effective it was to produce them, the M4 Sherman and the T34 could not quite fight a Panther 1 vs 1 but the amount of Panther or Tigers comared to the amount of allied tanks was more important.

In the end the germans were not godlike tank designers, there newly developed tanks were ok. The needed some more testing and production would have to be rationalised considerably.

The FAQs section should have some answers. Suffice to say it's a Hollywood trope; the Tiger and the Panther were horribly unreliable machines, and much of the actual killing in the war was done by anti-tank guns, infantry anti-tank weapons, and tank destroyers. Tank on Tank combat was quite uncommon if not rare.

No. They both fulfilled very different roles for very different doctrine. In straight tank-on-tank combat it was about even-at longer ranges German tanks would have a general but not absolute advantage, close range the allied tanks generally would win. In fact, id argue that the allied tanks were, on average, better. They generally had much more mechanical reliability, and were made with superior alloys, something that plagued the germans in the late war.

Since you mentioned Fury I will point out the scene in which Brad Pitt's Sherman engages the Tiger and has to work around it to get a kill shot (this is in the trailer) is misleading.

While it was true that a 75mm armed Sherman probably wouldn't penetrate the frontal armour of a Tiger even if the gun was touching it (I'd like to see if that was ever tested) the 76.2mm gun on Pitt's tank could penetrate the frontal armour of a Tiger tank at a range of a few hundred metres, which the battle did end up being fought at before it closed to the point blank range shown in the trailer.

Antony Beevor mentions in his DDay book that the terrain of Western Europe negated much of the superiority of German tanks such as the Panther and Tiger. These tanks were more suited to good tank country (flat terrain for quite a distance) and in Western Europe tank country could be lacking. This meant that flanking shots from ambush were quite common. The Panther especially had quite terrible side armour. Pretty much anything the Allies had could penetrate it. There was also a rather glaring design flaw in the early model Panthers in which hits to the lower gun mantlet, which was over 100mm thick, could deflect rounds downwards. If the turret was facing forwards this could deflect the round onto the thin (15mm) thick top hull armour, under which sat the driver, radio operator, the transmission and AMMO. This wasn't fixed until the Ausf. G model of the Panther with a redesigned gun mantlet but due to realities of production many Ausf. G Panthers ended up with the older gun mantlets.

The Tiger came out in 1942 and the Panther came out in 1943. Before that the Germans were basically outclassed by Allied tanks. That's a significant period of the war where the Germans had the so called inferior tanks.

In a tank vs tank scenario, yes the german tanks were far superior. But tank vs tank engagement were a very rare occurrence, american tank doctrine stressed that tanks should always try and avoid engaging enemy tanks, that was left to anti-tank weapons and tank destroyers. If, however a sherman did encounter a tiger, it would play out like you see in the movie. The Sherman's shells were too small and it's cannon had too little muzzle velocity to pierce the tiger's armor unless it got real close or managed to get behind and land a rear-armor hit, which was very hard to do given the devastating effect the Tiger's 88mm had on armor.