I'll add a little to it.. Sum it up a little more for you.
Lets look at the big picture. City of Columbus... Many officers.. sometimes not enough in the high crime areas. They often do not have enough time to do community patrols because there is too much "real crime" (as others put it) in these areas. Budget cut thin.. so.. no extra officers FOR patrol FOR those areas. This is unfortunately just the way it is. When you call in for accidents and other reports you often get sent to a phone recording instead, mainly to keep officers off these 'less important' calls as you could put it.
Another picture..
Outside areas.. your Hilliard, Dublin, Westerville, Gahanna, Grove City.. so on..
Excellent/Good/More than fair budgets for the police departments. They have plenty of officers per shift and can more than handle their run loads. You WILL see these officers patrolling because the tax payers DO DEMAND to see them. Invite yourself to a city meeting one time and youll be in shock over the amount of residents that roll in to complain about not seeing their favorite officers more than 1 time per shift drive by and wave. This is good community policing. You are paying for this community policing with your tax dollars.
When areas get too big too fast they often have troubles. Example.. City of Columbus sucks up a bunch of a neighboring township and doesnt put more cars on the road to handle those run loads. Good for tax dollars, tax dollars not spent on police officers for the area, crime goes up. This is simple math.
In your outside areas, land gets annexed, civil service tests for officers and bam you have at least 1-3 new guys to help cover the area.
No one dept does anything wrong or incorrectly.. they simply do what they can with what they have.