Which faction is stronger, or a template for comparing cities based on their strength!

How can you compare the Elemental University with, say, a library or a skeleton trainer? Each building provides COMPLETELY different advantages.

Yes, but without these advantages, the city takeover won't be complete.
And who said that the advantages would be "linear," i.e., easily comparable to each other? Here, you need to model specific situations.
If you're having trouble, create a specific battle scenario, and then everything will be more or less clear.