This is an interesting question, and fortunately not quite as complex to answer as it would have been had you not specified a particular time period, as although I have worked on armour throughout the Second World War, the level of technological change was monumental, and hugely complicates things.

When we consider solely the year period following the D-Day landings, the picture is somewhat more static, and thus a little easier to assess, and what becomes clear is that the Western Allies were served fairly well in combating German armour, despite popular conceptions. The M4 Sherman, although the subject of many tales, including the infamous 'Ronson' myth, as well as the A27M Cromwell, were relatively well-armed and armoured, largely reliable, and in some ways superior to the mainstay vehicles of the Axis forces - at this point, mainly the Panzer IV, which was beginning to show its age as consistent upgrades taxed the chassis.

However, where the Western Allies failed to match the Germans was in production of a heavy tank; although the M26 Pershing and the Centurion did make appearances right at the end of the war, their contribution was virtually non-existent. The Allies did develop some superb counters to German heavy armour, primarily the 17-pounder anti-tank gun, modified and mounted in the Sherman Firefly and the A34 Comet, as well as the 90mm M36 Jackson, but although these possessed significant firepower, none of them had the armour protection to be a complete match for a German heavy. Consequently, the Western Allies never had an AFV answer to the progressively heavier, more well-armed tanks such as the Tiger II which they were to encounter in the latter parts of the campaign, the result of which, as Buckley noted in his critique of armour in the Normandy Campaign, was the perception that Allied tanks were pitiful next to the Germans', an idea supported by incidents such as Villers-Bocage, in which noted ace Michael Wittmann and a small platoon of Tiger Is confronted and destroyed a number of British AFVs. Heavy Allied tank casualties, and heavy German tanks, as well as ingrained concepts from earlier in the war, combined to create this idea of the 'invincible Tiger', and a marked Allied inferiority.

This view however neglects to note a number of important factors, among which are the comparatively tiny number of German heavy tanks, not only in proportion to Allied tanks, but also in proportion to their own tank forces; Allied troops were far more likely to encounter a Panzer IV or a StuG III than a Tiger or a Jagdpanther. It also fails to note the multiplicative effect of the terrain on the success of German armour on the defensive, the Normandy Campaign's bocage country especially offering German tanks the chance to lie in wait and ambush, something the increasing preponderance of SPGs in the German forces, such as the StuG III, were suited to. With a high first-kill rate from the 75/88mm guns German AFVs fielded, the ability to get the first shot in from cover served to escalate Allied armour losses.

Yet perhaps the most important thing to note is that the largest proportions of Allied tank losses in Western Europe were not caused by enemy tanks - they were caused by anti-tank weapons, mines and hand-held AT launchers such as the Panzerfaust, WO 291/1186 putting these three factors as causing roughly 60% of British tank losses. American reports give AT guns an even higher percentile share of tank losses, highlighting one of the most important things to note - that armour did not exist in a vacuum. Although some German tanks were in many respects stronger than Allied AFVs, these advantages did not stack up to the Allies in other areas: they could neither easily replace nor repair their vehicles, and lacked both air and combined arms ground support. Thus, though German tanks made initial gains in both Operation Luttich in August 1944, and also the Ardennes Offensive in December, these attacks proved costly and were often blunted by Allied air and artillery superiorities, while the Germans could ill afford their losses.

Thus, although Allied armour was often weaker on a 1-1 basis to German tanks, though it should be stressed not all, its strength was based on its integration into a larger whole - where German tank forces could achieve tactical victories based on technical superiorities, the contribution of Allied armour was greater in scope; significant strides were made in infantry/armour cooperation, and armoured forces enabled infantry, which were arguably still the most important battlefield elements, to operate more freely. This perhaps stands some way in contrast to the Eastern Front, where the generally more open terrain allowed armour comparatively more freedom of action, thereby allowing them to have a more decisive impact.

I hope I've not derailed too badly from the question, and offered some satisfactory answers.

Sources

Buckley, John, British Armour in the Normandy Campaign, 1944 (London: Frank Cass, 2004)

Buckley, John, Monty’s Men: The British Army and the Liberation of Europe (London: Yale University Press, 2013)

French, David, Raising Churchill’s Army: The British Army and the War Against Germany, 1919-1945 (Oxford: Oxford University Press, 2000)

Macksey, Kenneth, A History of the Royal Armoured Corps and its Predecessors, 1914 to 1975 (Beaminster: Newtown Publications, 1983)

Buckley, John, 'Tackling the Tiger: The Development of British Armoured Doctrine for Normandy 1944', Journal of Military History 2010, Vol. 74, Issue 4, pp. 1161-1184

Zaloga, Steve, Armored Thunderbolt: The U.S. Army Sherman in World War II, (Mechanicsburg, PA: Stackpole Books, 2008)

The question is best answered by considering the phase of the war in consideration, then producing an overall evaluation.

At the opening of Barbarossa Soviet tanks were superior. A few months previously, a Soviet delegation had been shown the latest German armour and refused to believe this was the best, requesting to be shown the real latest developments. In 1941 the bulk of the Red Army's armour were BT-series high speed tanks, and T-26s, which was a slower tank based, like many others, on a Vickers design. Although often characterised as obsolete, the T-26 was loosely equivalent to the early PzIIIs and Pz38(t)s that equipped German units. The Soviets also fieled very light and amphibious tanks, and the multi-turreted monsters, the T-28 and T-35. In addition to these mainstays, early models of the T-34 and KV series had been deployed in small numbers.

While in terms of gun/armour/engine the Soviet tanks were on average superior to the German, with the T-34 and KV-1 being much superior, German tanks had advantages in radio communications, optics, durability, support, unit organisation, experience and organisation, and battle doctrine. Although victorious, the Wehrmacht suffered large casualties and some shocks when the first KVs and T-34s were met, notably at Rasyeinyia, Metsensk, and Tula, but Germany's advantages were more than enough to ensure victory.

During 1942 both sides suffered problems with availability of tanks. The Red Army had suffered massive losses in equipment and men and her factories were either under siege of being relocated, while the Germans too had failed to produced enough modern equipment for a prolonged war. The Soviets focussed on rationalising their roster and churning out as many T-34s and KV-1s and they could, while Germany instituted a crash program of mounting any gun able to defeat these tanks onto any chassis that would accept such a gun. A crash program was instituted which eventually resulted in the Panther, while the Tiger program was given top priority having been previously pursued at a leisurely pace. The PzIII and PzIV were quickly given long, high velocity guns. This eastern front arms race had effects in North Africa, where the British struggled against the small numbers of these new German tanks.

By late 1942/3, the time of Stalingrad, things were fairly even as the Red Army gained experience and skill, and their output increased, and the Germans struggled on with their improvised vehicles and still-superior handling of their armour. The victory at Stalingrad was a refection of this: Red armour swept around the city at speed, while a German relief column was easily brought to a standstill.

The Soviets then attempted to drive on and push the Germans out of southern Russia, but three Waffen SS units, freshly equipped with the latest vehicles, smashed their advance at Kharkov.

Kursk followed in July 1943, the Wehrmacht now equipped with the new tanks inspired by the original shocks. The Russians still fought with the original T-34 and KV series, now available in numbers. In a sprawling struggle, improved Soviet tactics absorbed the German attack and a massive counterblow was inflicted. In this period the Tigers and Panthers were almost invulnerable if handled carefully on the open steppe, as they could out-range the Soviet tanks and pick them off at will. But any attempt to attack or move in close, and this advantage was lost, and in any case the majority of German vehicles were the older types, no better than their enemies.

The rest of the war was a series of Red Army offensives using superior numbers of vehicles, while Germany moved its armour in a 'fire brigade' role, moving all around the front to contain each attack. She became less and less effective at this.

By 1944 the Soviets were re-equipping with up-gunned T-34s and improved heavy tanks, as well as many assault guns of the German style (which tended to be used as assault artillery rather than as tank destroyers). In mid-1944 German Army Group Centre was utterly devastated, and the skill difference was becoming almost negligible as German training was curtailed by fuel shortages. Sheer numbers became a huge problem, as the best German tanks could not be built quickly due to their excessively-high quality.

The first encounter with King Tiger tanks was a Russian victory, the T-34/85s on hand outmaneuvering their opponents who lacked the skill of their predecessors.

I have described a long period of fighting over a vast area of mostly open ground.

In contrast the Western experience of armoured war was short, and heavily influenced by a single campaign, that in Normandy.

It is easy enough to 'prove' that the superiority of German armour was over-rated, or even a myth. But this is to misunderstand the psychology of war, especially when one side has many fanatics keen to die for the cause, while almost all British and American soldiers wanted to get home. Yes, the Tigers and Panthers were a minority, but stories such as the experience at Villers-Bocage, or near Cagny when three Jadgpanthers knocked out several troops of Churchills (which had 150mm frontal armour!) without loss and drove past giving a mock salute to the panicked crewmen, had a profound affect on morale. It is very well to tell the tankers that their Shermans were just as good as the 'average' German tank and didn't really burn easily, but they saw platoons of their tanks smashed one after the other by an enemy they couldn't see, repeatedly. These crewmen knew their odds of survival were always counting down, and they would probably have no warning of their tank being in danger.

It was a failure of leadership that the Allies did not provide small numbers of a genuine assault tank for their men, and paid little attention to sharp end of the arms race on the Eastern Front. One problem was the disorganised way Allied tanks were developed, with one requirement getting in the way of another, again and again.

So whereas the PzIV was upgunned and uparmoured right through the war, the Cromwell- the first British tank with a serious, powerful engine, was obsolete as soon as it appeared in 1943, and could not take a larger gun than the low-velocity 75. Its many predecessors (eg. the Crusader and Valentine) were virtually incapable of development (and before anyone points out both these tanks were given larger guns, this was only by removing crewmen and neither tank had any relevance in upgunned form. Neither could take a decent engine).

In u/HereticalShinigami 's excellent answer it is pointed out the Pershing and Centurion were excellent late arrivals, and it was these tanks that took the 'big step' needed, but all too late. Compare this with the Soviets: their pre-war T-34 and KV were recognisably the antecedents of the T-54 and JS-III, which were formidable tanks well into the Cold War.