The Fledermaus III and the Ludwig cost roughly the same points (43 vs 40) and are both capable of taking out enemy armored units.
The Ludwig has unlimited range on its main gun and rolls more dice against Amor level 5, 6, & 7 units. It can also take advantage of cover on the battlefield to prevent itself from being targetted.
The Fledermaus only has range 4 on its weapons (but it can't be attacked outside of range 6). It also can't perform sustained attacks. Nor can it hide behind cover. However, it has move 3, can deploy almost anywhere on the battlefield, can move over any type of terrain, rolls a few more dice against Armor level 1-4 units, and rolls significantly more dice against infantry and aircraft. Oh, and it has two more health as well.
If you could only have one in your Axis army, which would it be and why?