How would you categorize the obligations and services of state and local governments as compared to those of the federal government?

Answer 1

yikes, where to start?
schools
police
fire
sewer
water
national guard
parks except national parks
roads except interstates
...... on and on

Answer 2

so cities and states concentrate on local issues while the Feds do wars and currencies and diplomacy with other nations. The feds of course may fund state or city efforts in local issues such as road or building or park construction but in theory the local people are in charge.
There is of course much overlap, such as city jail, county court and jail, state prison and court and Federal prison and court.