If your goal is to produce 300, 400 or even 500 hp from your small-block, it is always easier to reach said goal with more displacement. Taking things to extremes will help illustrate our dilemma. Suppose your goal is an easy 400 hp. Achieving that with a 283 will require some serious components, as the 283 must produce a 1.413 hp per cubic inch. Producing the same 400 hp with a 400-inch stroker requires a specific output of just 1 hp per cubic inch.
Back in the '50s, 1hp per inch was pretty impressive stuff, but add a set of aluminum heads and cam to just about any small-block today and you'll be rewarded with a minimum of one hp per cubic inch. Still, exceeding 1.4hp per inch with the 283 would require not only wilder cam timing and additional static compression, but also more engine speed compared to the 400-inch small-block. Reaching 400 hp with a 400-inch small-block would require less than 5,500 rpm, but look for peak power to occur past 6,500 rpm with the smaller 283.
What this means is that despite a similar peak number, power production through the remainder of the curve (below the power peak) will be skewed greatly in favor of the larger engine.
It is this last point that actually makes the stroker assembly so popular. The reason for the importance of the so-called area under the curve is that drivers spend much more of their time running through the lower rev ranges than they do at the power peak. Even in a drag-race application, the powerplant must rev through a given rpm range through each gear.
Acceleration will be based on the average power production over the given engine speed. Basically put, bigger engines offer more average power (even assuming the same peak power).
Adding fuel to the fire is the fact that building a stroker version that offers more cubic inches nowadays requires few (if any) additional expenditures, as a 3.75-inch stroker crank is roughly the same price as its stock displacement equivalent. Of course if you already have a 350, you'd have to step up to the stroker assembly, but additional displacement is always money well spent.
Strokers not only offer more average power, but they can produce that power with relatively milder cam timing. A wild cam in a 283 would be considerably milder in the larger 400-inch plant. Given the same cam specs, the stroker would idle better, offer better drivability and even possibly improved fuel economy if the cruse rpm was optimized at the lower rev range (made possible by the increase in torque of the bigger motor).