First off thank you for taking this question from /r/shitwehraboossay to /r/AskHistorians. I'm very sorry you haven't been able to get an accurate or timely answer, but I'll do my best to alleviate this. I just want to note that, despite you asking in specific about 'armor on armor' battles. There were few pure instances of this on the Western Front - my area of expertise, the discussion of how armored units behaved viz. units with no formal training alongside them cannot be separated in my view. Take this as you will.

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Part One

I know that in ww2 there were several factors playing on the battlefield: supplies, crew skills, air cover, quantity of armoured vehicles and At guns, coordinations of units, etc..

Okay so you already have a fundamental understanding of what truly provides tanks with the ability to:

eliminate the enemy armoured units?

So we only really have several areas of true 'armor on armor' or battles that involved 'armor' in any significant scale and scope on the Western Front (I will refrain from commenting on the Eastern front due to a lack of unbiased sources), the North African campaign in a very general sense, the Battle around Caen (June-July 1944), a sharp series of division-sized engagements between Orleans and Metz in August-September 1944, the Battle of the Bulge and the Ruhr pocket. For lack of space and time, let us focus on the Summer fighting of 1944, in which the oldest myths persist despite being definitively quashed.

One thing becomes incredibly obvious in all these engagements; terrain, organization and all-arms co-ordination are the biggest factors in allowing a unit equipped with a fairly well balanced tank model to operate with success. Notice I distinguish a 'balanced' tank model: Unfortunately for the esprit d'corps of the British tank arm, they are about to take a bit of a beating in this answer, but not without unjust cause and never in doubt of their bravery and willingness to engage the enemy:

Normandy: The Mutual Failure of Armor in the Attack

Unfortunately for the record of the Sherman tank, British historiography was the most visible in the years immediately after WWII, and British military historians struggled to explain the gross losses suffered in the many indecisive operations launched to outflank Caen on the Orne. In searching for an answer, they seized upon the perceived weaknesses of the M4A2 and M4A4 models leased to them by the Americans. In reality however, doctrinal shortcomings plagued the British in Normandy; and the British therefore continued to suffer heavily in the attack. Yet as it will be shown, when the Germans attempted to launch their own all-arms attack in the Caen sector, they often faced the same bloody repulses - and at the end you will be forced to conclude that whatever qualitative superiority the Germans held in their tanks guns had little decisive effect on their outcome of battle with their counterparts.

True, they had greatly improved the organization of their armored units by 1944, but the terrain and the manpower crises looming meant that an already sluggish combined-arms doctrine was doomed to allow for high losses, Max Hastings in his Overlord describes a key factor in explaining high British losses; no great deal of inter co-operation between Tank and Infantry in terrain that absolutely demanded it, describing the British repulse at Villers-Bocage:

....As Second Army reviewed the events of the past four days, it was apparent that the Germans had handled a dangerous situation superbly, while XXX Corps and 7th Armoured Division had notable failed to meet the responsibilities that had been thrust upon them. On 10/11 June, the division had begun its attack led by tanks widely separated from their supporting infantry. When they encountered snipers and pockets of resistance manned by only handfuls of Germans, the entire advance was blocked for lack of infantry close at hand to deal with them.

(Hastings, page 135)

Likewise, disaster was frequent for German attacks into such terrain, and it is of little surprise to me that Historians of note tend to not dwell too long on the 'abilities' of the Mark V and Mark IV when their results were so equally dismal more often than not in such terrain, from Hasting's Overlord again:

...throughout their long drive up the road to the battlefield that morning, even after the lifting of the cloud that hampered air operations for part of the morning, 21st Panzer suffered little material damage from Allied fighter-bombers.

(Ibid. 112)

It is important to keep this detail in mind, the 21st Panzer counter-attacked the 6th Airborne, a unit hopelessly outnumbered and lacking in organic artillery and often with little direct contact with the overwhelming off-coast fire support. The entire situation is not all too dissimilar to what the average German infantry unit would find themselves in by late July; bereft of fire support and forced to maximize the presence of what little manpower they have. Therefore in my mind, this stands out as a prime example to quash an often repeated (but outdated) piece of histiography; that the Germans handled their armor any better on the offensive in Normandy than their counterparts, and that 'losses' were due more to air-power than fighting on the ground of Allied infantry and armor. At the start of their attack, the 21st Panzer had 127 Mark IVs Hs, and a significant number of 'beute'(captured) excess armor from the defeated French. As the day carried on, and the German panzergrenadiers acting without their armor, stalled out in front of the Paratroopers, an armour on armour battle developed on the Western flanks, as the leading tank Brigades joined the fight:

The last important action on the British left on 6 June was the battle against 21st Panzer's armored thrust, an action which went entirely the way of the invaders... The Germans recoiled westwards on meeting fierce fire. When at last they encountered the heavily-gunned Sherman Fireflies of the Staffordshires on Hill 61, the consequences for the Germans were devastating. 13 tanks were immediately destroyed. Only a handful of 21st Panzer's tanks...reached the surviving strongpoints of the 716th [German Statik] Division around Lion-sur-Mer. By a dramatic coincidence, only minutes after they did so, the fly-in began of 250 gliders of the 6th Airborne Division to a landing zone eastwards, around St. Aubin... ...by nightfall, they were [falling back towards Caen] with the support of 24 88mm guns. But they had lost 70 of the 124 tanks with which they had begun the day.

Hastings is damning of the German effort in the bocage:

For all the dash with which Marcks and von Oppeln urged 22nd Panzer Regiment into action, its belated attack had been pushed home without determination or subtlety...

(Ibid. pg 116-117)

The death-ride of the 21.Panzer is not an abberation either; what of the later fighting when German premier divsions were hurled into far more determined and concentrated counter-thrusts? For this, we now turn to Kevin Baverstock and his Breaking the Panzers. It largely describes the fighting of the better part of the II.SS Panzer-Korps against the Operation Epsom bridgehead on July 1; and the narration of events gives a reader a sense of Deja Vu to the efforts of the 21.Panzer. The 9, 2 and elements of the 10 and 12.SS engaged units of the British 11th Armoured Division and 43rd Wessex Divison, South-East of Caen. The effort to destroy a salient gained by the indecisive Epsom ends in a bloodbath.

The conclusion of Epsom, an operation that went forward with little in the way of material air cover (the weather between 19th of June and 1st of July being highly unfavorable to co-ordinated air attack) never the less managed to threaten the flank of Caen. The Germans thusly counter-attacked, and the Tyneside Scottish bore the brunt of an armoured attack. The end results however? Dismal; all ground gained by the Germans were re-taken in local counterattacks and the SS could add at least 30 Mark IV and Mark Vs to their list of destroyed vehicles; already at that point well over 100. The total German losses in armored fighting vehicles for just under a week of localized fighting was nearing 150 vehicles, and the total loss of initiative after Epsom made many of these vehicles irrecoverable.

It is hard to conclude therefore that the Germans, despite in my view and the view of many other historians having a far more robust understanding of Combined-Arms warfare than the British, fared any better or worse than the British when attacking in such poor terrain.

Sources:

Breaking the Panzers: The Bloody Battle for Rauray, Normandy... Baverstock, Kevin

Overlord: D-Day and the Battle for Normandy: Hastings, Max.