The PPK/S is basically a PPK slide on a modified PP frame. The grip is slightly longer than a standard PPK's, which gives you marginally better control and a slightly larger magazine capacity at the cost of more difficult concealment, though the difference is small on all counts. Since the PP series are basically all concealment guns, I'd go with the standard PPK.
IMHO, a much better option is the Kel-Tec P3AT. It's still a .380, but half the size, one-third the weight, and much less than half the price. I have one, and I love it.
Full disclosure: Kel-Tecs have a reputation for having FTF and FTE problems out of the box, but the company invariably fixes them VERY quickly and at no charge when returned for service. This seems to apply more to first-generation guns than to current manufacture. I recommend the hard-chromed model; I've heard of very few problems with those. Mine is a HC 2nd-gen model, and I've put several hundred rounds of 10 different brands and styles of ammo through it without a single malfunction of any kind.
Walthers are made like Swiss watches, and they have that James. Bond cachet--but compared to the KT they're big, heavy, and expensive. I doubt if the BG you shoot with either will know the difference.