Assuming by performance you mean the total power or torque output of the engine, the displacement is certainly a major factor, but it cant be analysed individually. Other factors such as number of cylinders, number of strokes, Compression ratio, mode of aspiration, bore/stroke ratio, cam profiles/ timing, head geometry, redline,etc etc etc... when considered for a given displacement reveal the overall picture and are equally important.
A single cylinder 1000cc engine will have a entirely different performance figure than a 4 cyl, and a 1000 cc 2 stroke will behave highly unlike a 4 stroke, and with a different powerband.
And if the engine size, weight and NVH is also considered towards overall performance, a single cylinder will require a much heavier flywheel and thus a heavier overall engine. Also a multicylinder engine of the same capacity allows for reciprocating load balance and better vibration characteristics.
Along the same lines, a litre class bike engine has a horsepower figure of around 190 HP, whereas a 1.2 L car engine could peak at sub 100 HP. What makes the difference in this case is a higher redline and a different bore/stroke ratio.
Displacement also doesnt reveal a correct picture when forced induction comes into the picture. Small displacement turbocharged engines make much more power than NA higher capacity engines; current 1.6L F1 engines are the smallest ever displacement wise, but generate the highest power ever, all thanks to turbocharging.
And then race spec versions of road vehicles having the same engine with the same displacement churn out entirely different numbers. ECU fuel and ignition maps matter too. A lot.
In all, displacement alone isnt enough to predict the engine performance, knowing at least the 3 other factors described above as well can help get a clearer idea. And in the end it always comes down to what application the engine is designed for.