The examples given are not clear though and have nothing to do with unit or ability balance but only map design. A Jagdtiger performs the same in 1vs1 as it does in 4vs4 the stats are the same they don't change. A Jagdtiger is meant to send long range projectiles towards enemy armour which is it's purpose and it performs this in 1vs1 , 2vs2 , 3vs3 and 4vs4. You may have to adapt your strategy to suit the map but this is the case with every game anyway.
Yes this is largely correct, both the map and the units are factors. The JT (using the example) is an absolute necessity for at least 1 player in 4v4 modes but its effectiveness depends on the map as you say. But if you were playing 1v1 the JT doesn't really fit any clear position in the game; sure it performs the same roll but that roll is going to be needed very rarely.
Or in a smaller map like the port, you play in 4v4 team as OKW and through no fault of your own you end up with 3 other OKW players. On a map that small with so many base trucks you are all going to suffer heavily from a CalliOP or Land mattress through no real fault of your own; just down to the random team set up and the map chosen by the match maker. But in 1v1 on the same map the unit would not over perform so much. So it is certainly a combination of both things.