I read in Gerald Janusz's book Algebraic Number Fields where he says there are two approaches to class field theory. The traditional approach, as in his book, uses L-series, Dirichlet density and Frobenius density theorem, to prove the surjectivity of the Artin map. Then with only a little bit of cohomology without talking about ideles one can prove Artin reciprocity, conductor theorem, classification of abelian extensions etc.
I also found many other books, for example the one by Cassel Frohlich, that avoid analysis technique and prove these theorems by systematically using cohomology and ideles classes. I guess this is the modern approach to class field theory.
I wonder what are some pros and cons for these two approaches. For example, the traditional approach won't require many advance algebra techniques and the modern approach is more insightful(for example, we define Brauer group with cohomology). Plus, I guess the modern approach is more generalizable, for example to function fields. But I cannot find many useful resources on class field theory on function fields. Is there any references? Thank you.