My parents have always divided up responsibilities.
My dad has always managed the finances. He loves math and likes managing money, my mom doesn't.
My mom was mostly responsible for my sister and I when we lived at home. She usually took us to and from school, took us to extracurricular stuff, took us shopping, etc. My dad has definitely been involved in our lives, but not in the same capacity as our mom. Dad's big thing has always been college...not for sports or anything, strictly for academic reasons. We both graduated in four years and my sister decided on her own to follow it up with a master's degree.
When my dad maintained the cars himself, he took care of all of them. By that I don't mean checking oil, tire pressure, etc though. My mom has always done that herself on the vehicles she drives primarily. She knows how to do an oil change, just no interest in doing it, so my dad did take care of that. When he decided he didn't want to do maintenance himself anymore, they divided the tasks. My mom takes care of her cars and my dad takes care of his. Vehicle decisions have been a mixed bag. Some vehicles were shopped and decided on by both parents such as the Cherokee and Rangers. Other cars were independent choices, such as the Civic Hybrid (dad's) and Mazda 3 (mom's).
My dad does the majority of house maintenance and repairs, and cleaning has usually been split evenly or delegated to my sister and I. My mom makes basically all decisions regarding the yard and landscaping though. My dad will pitch in and help with the work, but he isn't interested in the planning of it. My mom is more than happy to do that anyway.
They have been married for over 38 years, so it seems to have worked out.