The attributes should be selectable: say this

You are ___(Zulu)
You have 50 attribute points to distribute among the
realms of

Attack Bonus (costs 2 attribute points for 1 bonus)
Defense Bonus (same as above)
Air attack Bonus
Bomber Bonus
etc.

The computer teams select the attributes randomly.

Civ A has a bank in, say, 80% of its cities. As a result it gets a +10% cash bonus.
However civ B has a higher percentage of its cities with banks than anyone else in the world- in fact every city has one. Therefore it gets an additional +10%, as well as the bonus that civ A has.

Meanwhile civ C has been building up its Army. It has the most barracks, giving +1 defense, and 85% of all its units are army ones, giving +1 attack. However civ A has the best infrastructure in the world- the highest ratio of tiles with railway to tiles without (within its borders). This gives its land units +1 movement, to show logistical expertise.

Civ B, being an island one, has a large navy, making up 65% of all units. As a result, its ships have +1 attack. It also has a port in most of its seaside cities, giving +1 movement.

This approach has several advantages in my opinion-
1) It encourages empire wide development, so that we would see less of cities with practically no improvements in the modern era, even if they are small.
2) It allows smaller empires to have more power- allowing nations like those of Western Europe to be represented accurately.

In a random map, you could land on an island as the germans and would get the bonuses the english would get on the world map

Obviously on the world map they would alwasy be the same