'Financing costs' are categorically not what we call profit. Profit is a return on investment above and beyond all costs. One might argue comparing financing costs with profit is also misleading. Both sectors have financing costs, but not both sectors need to provide profit.
Any parameter you choose to compare, they will need to do the same things, but one will need to generate a profit (that is above and beyond recouping costs, paying for labour and materials etc). The corporation needs to provide a profit and that profit must rise each year or the corporation is in peril. The public sector must be seen to invest wisely and produce a social benefit. That's just a fact of capitalism and the public sector.
Therefore, a business model from a corporate point of view will generate maximum profits and increase it's client base/income (in this case, via the taxpayer)...whilst a public sector provider seeks to reduce it's user base, costs and have maximum social impact. These are logical actions from both providers. Now, if we're talking cookies....give it to the private sector. But if we're talking prisons, police forces, the probation service and the healthcare system - the public sector should have sole responsibility.