Assalamou Alikom Warahmatou Allah,
I think that the very fact of saying "different school of thoughts" is little misleading. Indeed, two different school of thought are basically two fundamentally different systems of thinking and reasoning which might be even diametrically opposed in every aspect (think of communism and capitalism).
The Islamic school of thoughts (an inappropriate appellation in my opinion) or "Madhab" do no exhibit such patterns since they are basically the same in the sense that they all agree on the fundamentals but differ (and NOT disagree!!!) on the secondary issues. For example, regarding Al-Salat, it is well documented that our Prophet PBUH prayed with his hands crossed over his chest and sometimes he did not. Al imam Malik Ibn Anass said that it is allowed then to pray with hands loose while others said it is better to cross hands!
Note that both are right but each Imam preferred one situation over another. Hence, It is misleading to say "different shcool of thoughts" as if they were fundamentally different!
Now with regards to Islamic books dealing with this issue I do not know of a good English book (all books I know are in Arabic!) although I suspect that Dr. Bilal Phillips might have written something on this.
Wassalam