What are the advantages and disadvantages of Mezzanine debt versus Equity Investors in completing a Capital Stack and filling Gap Equity?

As a self funded searcher I am working through the structure of each and in modelling it seems like the Mezzanine would provide greater equity for the searcher and greater returns. So why not focus on that structure?

Am I missing something here? Seems like most interest I see on posts are for equity investors to fill the gap.