With combat based upon a differential between the gun value and armour value, it can be seen that a Tiger attacking a T-34 would have a differential of +4 whilst either a KV-1 or a T-34 attacking a Tiger would have a differential of -2. To add to the lethality of the Tiger, as with all German vehcles, it gets to shoot twice per turn compared to the Russian once per turn (prior to 1943 anyway).
First manufactured in 1942 and remaining in production for 2 years, the Tiger was not the best tank design of the war but it can probably lay claim to being the most famous.

The need for having a heavy tank was brought sharply into focus during the German invasion of Russia in the summer of 1941.
Here, the panzer crews met the formidable Russian T-34 and K-V1 tank designs, which totally outclassed anything the Germans had with regards to armour and armament. For a time, up gunning the Panzer III and IV allowed Germany to maintain a parity in the gun / armour race but it took the arrival of the Tiger tank to restore confidence in German technical superiority.

The first Tiger battalion sent to the east front arrived in time to participate in Manstein's Operation 'Winter Storm' in December 1942, they gave a good account of themselves and compared to the many lighter vehicles on the battlefield (from both sides) their power must have appeared awesome.
The Panzer Grenadier game (Russian Front 1941/42) comes with a single Tiger counter (platoon strength). 'Heroes of the Soviet Union' adds an extra 2 counters which gives us a whole company, which 'Heroes' puts to good use in 2 of the scenarios that deal with Kursk.

In practice, the lumbering Tiger can move around the Panzer Grenadier battlefield of 1942 fairly immune to interference from anything else.
The closest competitors from the Russians are the T-34 and KV-1 tanks (short guns) and even they are likely to be short lived in the presence of the Tiger. The values on the counter are as follows; 'red square box' the armour rating, 'yellow square box' the anti-tank ability showing strength / range, 'black letters' the direct fire (H.E. & MG) ability showing strength / range. The number in the top right corner is the movement allowance. 
Of course the Tiger does have some enemies. It is as vulnerable as any other vehicle in close assault situations especially in built up areas or woods and without infantry support. It is quite slow and some of the faster soviet light AFV's can move around it's flanks to set up crossfires (representing flank shots) - essentially reducing it's armour value by a factor of 2.  The Guards 76.2mm artillery is also a threat as it has an attack value of 6 - narrowing the differential to an attainable level (but even here, the firer would need to score 11 or more on two dice). And finally getting adjacent to a target brings a combat modifier but trying to get adjacent to a Tiger might prove an expensive and unfruitful tactic.
Until the Russians get some heavier firepower, it isn't too much of an exageration to say these things can roam at will and it is easy to understand how their initial impact and superiority left the vehicle with an enduring reputation of invincibility.
TIGER TRIALS - 1942
The following four trials were played out to test the Tiger on the Panzer Grenadier boards. In making any analysis, remember the variables caused by the dice rolls - double sixes, happy days - but overall an average impression should still be possible.

TRIAL 1:
9 x T-34A platoons advance on a Tiger 1 platoon over fully open terrain. The basic rules of the trial are that both sides have an initiative level of 1, a morale level of 8 and that the T-34s must make very effort to get adjacent to the Tiger for the adjacency modifier and if possible try and create a crossfire (flank attack). The T-34s set up just outside extreme range (13 hexes).

RESULTS: This was quite a good result for the Russians, they eliminated both steps of the Tiger platoons and lost 6 steps themselves in the process.
Verification tests: range from the T-34s losing just 2 steps to being wiped out - the variables tend to be in the 'charge' part of the trial, once the T-34s are in firing positions, things even out.

TRIAL 2:
As above but the Russians were reduced to a much more realistic 6 platoons of T-34s.

RESULTS: All 6 Russian tank platoons were destroyed (12 steps) the Tiger remained intact. Several of these kills were due to the ease at which the Tiger can knock off a step and then 'disrupt' a T-34 at range (meaning the T-34 could then only move 1 hex per turn OR attempt recovery) giving them more shots at those targets while they were held at bay.
Verification tests: consistent, the T-34s don't stand much of a chance.

TRIAL 3:
As trial 2 but this time, the six tank platoons would charge out of a wood onto an unsuspecting Tiger.

RESULT: All 6 Soviet tank platoons were lost, the Tiger was flipped, losing 1 step. This could have been a better result for the Soviets but they quickly lost their position (through elims)  that gave them crossfire advantage - better luck next time !

Verification tests: The Russians defeat the Tiger, losing as few as 2 steps themselves, maintaining firing positions is the key (crossfire).

TRIAL 4:
A Russian infantry company consisting of a leader and 3 x 4-2 platoons close assault a Tiger platoon in the open.

RESULT: On their first round of fire, they get lucky and roll a six, this flips the Tiger (had they been a 6-1 SMG company, they could have fired on the next column up and that '6' would have caused two flips, which would have seen off the Tiger). 


After 4 turns of assault, the Tiger has not taken further loss and the infantry company is ordered as follows;
Time to retreat and hand the fight over to someone else.

Verification tests:
confirm a step loss to the Tiger and then a deterioration of the infantry over 4 turns.

Although these trials were not particularly sophisticated, they do highlight some points of note.

GERMAN PLAYER: The Tiger is powerful and does not need the adjacency modifier itself, it performs best when fighting at arms length, particularly in the  6-8 hex range bracket. Whenever possible, it should attack full strength units as it stands a very good chance of eliminated both steps in a single fire.  The biggest danger comes not from adjacent units but rather from any enemy that is able to set up a crossfire attack, look for these potential attackers and hit them first even if a better or more obvious target is available.

RUSSIAN PLAYER: The all out charge to cover as much ground as possible may be tempting and if the map is very open, then probably essential (trial 1). But a planned approach using cover and having part of your force (good job for light tanks) work around the enemy flanks to get the crossfire modifier is probably going to be the most cost effective way to do it. If you can force the Tiger platoon to move to avoid being outflanked, then all the better as it's slow and can't move AND fire in the same turn. You will have to be very lucky to make a successful attack without loss and the above figures suggest that even a 6:1 ratio of units is no guarantee.

Finally, the infantry assault can be effective but a good precaution would be to have a second infantry stack nearby to relieve the assault troops. Also if the Tiger has it's own infantry with it, think twice about close assault or consider dropping artillery onto the hex before assaulting it (but remember friendly fire risks !), to clear the infantry away.

In 1942 at least, the Tiger is queen of the battlefield and as such comes with the warning - handle with care.
Leader  OK
Platoon 1 demoralised
Platoon 2 disrupted
Platoon 3 flipped and disrupted
The Tiger tank
Panzerkampfwagen VI