Saved Search is more flexible when it comes to formulas and conditions. You can add several formulas with complex conditions to pull up the preferred results. While Report is used for pre-built report definitions that you can run to review, present, and analyze your account's data. It is more reserved when it comes to formulas and conditions.
The advantage of Report from Saved Search is that it has Historical Data. Historical Data is important when reporting financial data. If you use a Saved Search to pull up a specific sales order transaction for example, you are only allowed to pull up its data that you can see on its record on today's date. To further explain, if it has a different balance on February 2020, and you decided to pull it up from a Saved Search on March 2020, you will only see its balance for March 2020 no matter how you change the Date.
Unlike when doing Reports, it is based on the transaction's Financial History and Period. This enables you to pull up a report that shows the changes based on Date/Period. By using Report, you can pull up the balance on a certain period or date.
If you are creating a report and doesn't need historical data, you can sort to Saved Search for a more straight forward reporting. If you are creating a report for your financial data and requires to get the exact amount based on the Date Period you're selecting or the status and other information that should be based on Historical Data, you should sort to Report.