Sure the Shadow have more Army symbols. The dice are not meant to be identical between both sides. The shadow dice are more War-ish which I think is very thematic! On the other hand the Free Peoples have more Character symbols (which they need) AND don't forget the Will of the West which is a huge bonus for the Free Peoples.
In some ways, while I'm not a 100% tolkien expert, the way I often view things in Middle Earth is that the Shadow forces tend to be more aggressive, more based on hordes of armies, but not necessarily based on cohesive leadership. Thus, they get more army moves, less character moves. They don't depend on Leaders.
The Free People, on the other hand, are more peaceful; while they can muster themselves up on occasion, it's the leaders (both the famous ones like the Companions, and the lesser ones like Eomer and Faramir) that drive the people to action - thus the Character actions (which let you move armies with leaders) are more prominent (well, and the Characters moving with the fellowship too, of course)