Good question. The majority of German tanks in general were deployed against the Soviet, but the Tiger started to appear in 1943, when the West was beginning to engage the Wehrmacht on a somewhat large scale.
This website gives a quick history for each Tiger battalion (the Tigers were conveniently regrouped in specific units). I'm too lazy to track every number, but for what it's worth, I count 7 battalions that went to the Western Front, 8 that went to the Eastern Front, and 5 that went to both. That seems surprisingly even.
Good to know. I guess I had this image of 75% of Tigers facing the Soviets, but the battalion figures don't bear that out.
I have no idea why people are so crazy about tanks vs. tank engagements. Last time I checked, war was waged between many kinds of weapons and all of them had different tasks. The job of killing tanks was not primary duty of tank. There are many other means of stopping them.
More specifically, different tanks had different missions. And even in HOI3, the vast majority of battles in the game did not include tank on tank fighting.
But...
Tank on tank battles were often decisive in HOI3, if only because no one can really afford to see multiple armor divisions retreating or taking heavy losses. Even the USA, who can replace losses easily, still needs to win battles to maintain a foothold in Europe.
During the actual war, major campaigns and tank on tank battles ended up being decisive, if only because both sides wanted to put their armor at the schwerepunkt. So the tanks end up appearing in major battles, because otherwise they weren't being used properly in strategic terms. If the tanks weren't at a major battle, then they were a huge waste of supply and fuel.
Still, an argument an be made that having lots of armor in general to put into lots of battles (not just a few key battles) is a virtue in and of itself. Even if you think the Sherman was a piece of crap that could be destroyed by poking it with a sharp stick (I'm not saying it is, I'm just indicating that someone could think it was), having twice as many Shermans as the OPFOR has tanks means that you can do more than overwhelm the enemy tanks. You can also apply armored thrusts to softer formations
while still tying down the enemy's armor in tank battles, regardless of whether you win or lose them.
As always the answer is StugIII. Fantastic vehicle. Only thing that tops the M4 and T-34.
Everyone loves the StuG.