AArm and Arm are the sum of products of the numerical strengths and individual quality of target and shooter. It broadly correlates to 'firepower superiority' in a 'bloodless' exchange, and the higher values will tend to be superior.
Casualties are possible, even when there is no likelihood of penetration of front, flank or rear armour by accumulating sufficient 'crew casualties' to force the abandonment of equipment. This is rare, but observable, but may require additional situational factors. Equipment will also be abandoned in retreat/routs when in close contact, and these are more likely when there is an AArm>Arm superiority.
To obtain reliable casualties, the actual penetration of the weapons firing should exceed the frontal armour comfortably. While unit facing does affect vulnerability, it isn't quite as deterministic as a tactical game would be ~ there is a range of kill probability based on average/min/max distances to the unit footprint, and flank/frontal armour biased according to the general facing of the unit (most of the time there will be 5-15 armoured elements within the unit, and each may be facing in slightly different directions and be at differing distances ~ this is modelled 'loosely'). You can expect casualties at a low, but reliable rate if the flank armour can be penetrated marginally... depends if you can get lucky, or concentrate enough firepower to obtain a decisive result (on either morale, cohesion or casualties) to drive off a superior enemy before his counter-fire disperses your forces.
Note that while 1944 German Panzer forces are mostly homogeneous (with the exception of BfTB/HTTR Pz Rgt HQ), Allied medium tank formations and the German '41 formations tend to mix types - Sherman 75mm with either 76mm or 17 pdr, and 'Jumbo' heavy assault tanks ~ Cromwell with Challenger ~ Cruiser gun tanks with Cruiser CS tanks ~ Pz II and III, and Pz II and IV etc.
Here you will maximise effectiveness by closing to ranges at which the weaker vehicles are effective, but by doing so you increase vulnerability of the entire formation... it is a judgement call whether the increased offensive power is worth the increased exposure (which can also involve exposure to fire from more directions).
You can examine the data for elements listed in the E&S screen. It is possible to view your own data at any time, but if you want to view enemy equipment data, you should first pause the game timer so that intel doesn't refresh and close the window while you are trying to read it...
Double-click on an entry in the E&S tab to examine the weapon/vehicle information. Double click on weapons listed on the vehicle page to see their information...