If the Allies had a tank in 1944 comparable to the German Tiger, would they have won the War in Europe faster?

No not really. The length of time it took to beat the Germans was due to two key factors. Stalin underestimated the German threat prior to Barbarossa and when it did happen, his army had been purged of most of its competent generals. That he was able to re-group and move all his industry east by 1942/3 was a miracle in itself. On the western front, things were always going to take ages. A channel crossing was being discussed by British planners from 1940 but Chief of General Imperial Staff Allen Brooke realised that the Royal Navy could not guarantee supremacy of the Channel while the Luftwaffe operated from France. Furthermore, the Germans had several divisions to hand in France which would rapidly destroy any concentrated allied landing on the French coast. The raid on Dieppe in 1942 confirmed this. The other problem was shipping, in that there wasn't enough available for cross-Channel operations. So, Allen Brooke convinced Eisenhower and the Americans of the importance of clearing the Germans out of Africa with a view to freeing up the Meditteranean and allowing an invasion through Italy, which was in a more precarious political and military position than Germany. To speculate on the difference one piece of equipment would have made to such a large outcome is probably futile given the larger context described above. However, if I was to get into such detail, it is interesting to note the Battle of Kursk saw the biggest tank battle of the war and the total annhilation of the Germans.

In reply to the Panzers, Allies had many superior equipments in other arenas. That didn't sped things up. In fact the sophisticated Panzers were at a disadvantage against Russian T 34 / 44 s

I do not think so, as terrain and weather were the major slowig factors of the allied advance. Less rivers out east, hence less rivers to cross, and that is why Russia won the race. Their tanks sucked, and they still beat us there because of the terrain beneifts and the weather factors favored their advance. If the Russians had attacked from the west, they never would have breched the rhine.

The russians had greater numbers of tanks, anyway they could have won the war faster if they stopped Hitler @ czechoslovakia and not waited for the invasion of Paris.

I don't think it makes a large difference. By 1944, Germany is just exhausted from being at war and it is really only amount of time before they lose regardless of a tank or not. Though it might of made it quicker.

the war was over after a few months -> fast enough 4 U ?

That's a good question. From what I have read about tanks and tactics, I would say that having a tank comparable to the Tiger would been a great help, no question about it. The two things that made the Sherman so bad was that 1: they were powered by a gas engine. This caused them to burst into flames after being hit. 2: They did not have a gun capable of penetrating the frontal armor of most of the tanks that the Germans were using, not to mention the Tiger. The only advantage , with the Sherman, was its use in numbers. It would be useful to mention that the construction of a Tiger took over one hundred thousand man hours to build, was extremely expensive , and was unreliable. Very few were produced, as oppossed to Shermans , T-34s. The Germans would of been much more of a problem if they would of copied the T-34. It was so easy to manufacturer and use. The Tiger was too big , underpowered, and way before its time..

I don't think the quality of the respective tanks had much of an influence, if any, upon the speed of closing out the war. With limited fuel, lack of air support, and the preponderance of allied artillery, the German tanks were pretty helpless against the onslaught. They were chewed up by bombing and artillery. Yes, in individual battles and skirmishes, they proved superior to the US tanks, but the overall difference that made was, IMO, negligible.

Alot of people forget that supplies are urgent when waging war. It's much harder to advance than it is to defend. Then when you get past the defenses you must re-supply your advancing forces. The WW2 era intel couldn't keep up with advancing forces as they are in the modern era. Tanks in WW2 were really already becoming outdated with the use of airwarfare. Don't get me wrong they were important in ground battles but the air force could reach out an touch the Germans from anywhere. Of course, the battle would have been quicker if we had better equipment so to your question yes quicker.