The answer to that is yes and no. Yes a 2.8 is usually more powerful than a 2.4. NO its not always more powerful. There are many factors that determine an engines power output. Its a little thing called Volumetric Efficiency. Typically the more volume you have the more power you get,however if you take a smaller volume engine and increase the air flow into and out of the engine you have increased the volumetric efficiency by packing more air into the cylinder. As an example, lets say that you have a 2.8L engine with which has about 28.8 cubic inch's of volume in each cylinder, if the air intake system(filter, throttle body, intake manifold, cylinder head) is restrictive, the cylinder will not get the full volume of air. The cylinder created a vacuum effect which draws air/fuel into chamber. The more restriction in that flow the less power is produced. So if the engine only draws in 23.5 cubic inch's of air then the engine is said to have an 81.6% Volumetric Efficiency, so theoretically 5.3 cubic inch's of air is lost due to the restrictions. So if the engine theoretically makes 200 hp with 100% Volumetric Efficiency, then the loss of 5.3 cubic inch's of air per cylinder multiplied by 6 = a reduction of 31.8 cubic inch's, and the final output would be recuced by 36.81 and would have a total power output of 163.19 hp.
Now if you take a 2.4L (145 cid), with each cylinder having a volume of about 24.16, and you improve the air flow in and out of the engine, you may be able to get a Volumetric Efficiency of 99%. So with a Volumetric Efficiency of 99%, the engine only suffers a 1% loss of power, so each cylinder is drawing in 23.92 cubic inch's of air/fuel. If the engine theoretically produces 171.43(same ratio as a 2.8), then the 1% loss would only reduce the power by 2.9hp, and the final output would be 168.53hp.
So you can see by this example that a smaller engine can produce more power, however it must be made more efficient than the larger to do so. That is why 4 bangers with turbos can produce so much power. If a turbo can increase Volumetric Efficiency to %'s as high as 140-150%, then you could theoretically take the abover two engines and give them both turbos and they would both have a 150% Volumetric Efficiency, then the 2.4L would theoretically produce 257.15 hp and the 2.8L would produce 300hp.
The point in all this is to show that is isnt necesarily the engine size that dictates its power output, many other factors effect the output through Volumetric Efficiency and design.