Ultimately, both Slim designs were meant to expand the userbase from the core to mainstream gamers, but under different circumstances.
When they originally launched, the PS2 and PS3 had the appearance of "bad add tech"; the sleek design, the metallic case, and all the hype making them out to be the latest and greatest, gave the PS2 and PS3 a very "unconsole" like appearance. While this made the "computer entertainment system" more approachable to the hardcore, there are many for whom "bad ass tech" is actually a turn off, namely the more mainstream/casual gamers. Making a Slim version of the consoles, making them smaller and using plastic instead of metal, changes the appearance from "bad ass" to "toy", and makes it more approachable to the non-hardcore. Meanwhile, the hardcore don't care that much, it's the games that really define the console, the hardcore games were already there, and they already have their "bad ass" version; so who cares if a more "toyetic" version appears.
The real difference is the circumstances surrounding the Slim upgrades. When the PS2 Slim came out, the original had the hardcore/core market locked up, so the only place for growth was into the mainstream/casual space. When the PS3 Slim appeared, the old PS3 was in tough competition with the Xbox 360, giving them little room to maneuver in the hardcore space, and the Wii leapfrogged them right both in the race to the masses, so Sony had to give chase before Nintendo had them on lock down.