This is a very tough question, but I'm answering based on experience. For me it should be both - a teamwork.
Currently, I'm the bread winner for the family and my wife manages the finances. For our case, I work as a software development engineer and my wife is as a full-time housewife - she takes care of our children and manage the house which is already a tough job.
Honestly, work is already mentally draining and I won't be able to handle our family's finances. As such, our current setup is I provide (earn or put the money in) and my wife handles majority of what goes out. I just take a portion of it as my allowance for me to be able to come to work and eat.