By the screenshot I'm guessing you're building a financial report or modifying an existing one? Those don't translate well to saved searches, but for any other type of report than Financial (on the off chance you're not building a financial report), I would start with a saved search and only switch to a report when I find something the Saved Search can't handle.
The only time I really see reports "win" over saved searches is when you need to run something "as of" a certain date like an Aging report. Saved Searches can't really do that, but in nearly all other instances, I'd use Saved Searches.