In general, how do aircraft handle differently in inverted flight versus in upright flight?
Typically, unless the CG is quite far aft (as is often the case with aircraft designed for aerobatics), lots of forward stick or yoke will be needed to keep the nose high enough for sustained inverted flight. With inadequate forward yoke or stick input, the airspeed may increase very quickly as the flight path curves earthward and altitude is rapidly lost.  

This orange radio-controlled model glider doesn't even have ailerons, and it has a flat-bottomed airfoil, yet it may be flown in sustained inverted flight.  (Roll control is challenging-- inverted, the ample dihedral is very destabilizing.)  With the right technique, nearly any aircraft would likely be controllable in sustained inverted flight.  Getting there safely from upright flight, and getting back safely to upright flight afterwards, may be another matter, especially if the roll rate is sluggish.     

Obviously, whether or not the engines will receive adequate fuel and lubrication to keep running during sustained negative-G flight, and what will happen to the flight controls if they do not, will vary from one aircraft to another.