Question

who had won the struggle for power in Europe among the monarchy or the Church

Answer 1

It's hard to call winners and losers. Both the church and the monarchies increased their wealth and powers in the high and late Middle Ages. I would say that it was a win/win situation, because both the church and state (or proto-states, if you will) were well on their way to extricating their jurisdictions from one another.

You could write about secular courts and canon law courts, the end of the struggle between the Guelph's and Ghibellines, and the development of (and opposition to) tithes and taxes. Hope I was able to help :)

Answer 2

I think @Joel_the_boss did an excellent job explaining this