In real-world driving, it's not necessarily the peak number (horsepower, or even more importantly, torque) that counts. Rather, graphing out the torque and horsepower curves, it's the area under the curve which is really important. Despite the seemingly close peak horsepower numbers, the 2.3l has a far broader, stronger, and meatier area under the curves than the 2.0l. This can be felt in real-world driving (though the 2.0l is no slouch, especially compared to a lot of the low hp and low torque competition).
Having said that, there is one more factor and that is gear ratios. Knowing the gear ratios can give an idea of what aspects of the engine curves are emphasized, but one has to drive the car to really get the full feeling.
Of course, the 2.3l also has disadvantages, namely weight and fuel efficiency.