Owner’s earnings is often quoted by Buffett. The way he looks at business’ earnings is by looking at its reported earnings minus off non-cash items such as depreciation and amortisation then minus off maintenance capex.
The main difference is that, owner’s earnings captures the actual cash flow of the company that can be distributed back to shareholders (i.e. similar to free cash flow) where as net profit alone might not necessarily translates into dividends since some sales are made through credit.
The challenge again is assessing the maintenance capex of a business. Most companies tend to lump development and maintenance capex together and thus, making it difficult to precisely estimate the maintenance capex.