The main aerodynamic difference in inverted flight, from a pilot's perspective, is that the rudder operates in what the pilot might assume is the "wrong sense".
For a coordinated upright turn, you use right aileron and right rudder (matching inputs).
For a coordinated inverted turn, you use right aileron and left rudder (opposite inputs).
There is a good explanation of this effect in
Neil Williams's book,
Aerobatics.