There are some interesting answers.
Technically, yes you would need double the displacement with a 4 stroke to equal the power potential of a 2 stroke. Every time a two stroke piston comes up in the cylinder it is a power stroke and it exhausts on the down stroke. A four stroke engine's piston goes up and down twice before a power stroke. So for 2 engines with the same displacement (2 vs 4 stroke) the 2 stroke will have twice as many power strokes as a 4 stroke. Four strokes make more torque sooner and can rev every bit as high as a two stroke. (think formula one engines) 2 strokes are lighter, have less moving parts and are easier to work on.