My vote here goes for the PPS. I was really looking at both of these pistols before I made my choice as well. The Kahr is a bit smaller. In the end it really came down to the reliability of Smith & Wesson Customer Service backing the Walther product.
I ended up finding a decent deal on a used PPS with 3 mags (1 of each size, which was perfect.)
I put about 250-300 rounds through it over 3 range trips. The gun shoots very accurately. Recoil is much better than I would have expected from such a small gun. I did, however, have multiple failures to extract the spent casings, stovepipes, and a few failures to lock the slide back (although I believe that was me riding the slide release). The trigger was also very gritty and heavy.
I called up S&W Customer Service and explained the issues I was having with my new-to-me-but-used pistol and asked if they had any suggestions as to what I should try. The man that I talked to immediately offered to send me a pre-paid FedEx shipping label and said that they would take care of the issues.
When I send the gun in last Thursday(6/24) I included the note describing the problems that I am having. I also put in a request to have them install night sights and to call for a credit card number, if needed. I haven't heard back yet, but it's only been a week. I am confident that they will resolve my issues and assuming that all is well, I will probably have the PPS done in Robar NP3 coating.
All things being equal, you can always rely on Smith & Wesson to take care of you. I have not owned a Kahr, but I hear that they are great guns - if you get a good one. You will find numerous stories on here about people who send their gun back to Kahr several times without having their issues resolved. I can not personally attest to this - but I am very confident in Smith & Wesson..... and that alone was probably the deciding factor in my choice of the Walther PPS.
Good Luck!