I'm not sure. Saratoga was returning to Hawaii during the Battle of Midway so she never directly engaged Akagi. They're both from the same generation of converted battlecruisers so I guess you could see them as pre-war rivals but that's about it.
Seeing Akagi square away the burgers at lightning speed and downing Hiei's curry probably made Sara like that as a cook and as an observer remembering Lexington going down from multiple strikes (though isn't seeing someone down a crapton of food a good thing or somefin?)
