Of your two alternatives, I would pick the Sig P220, and would probably go with the new "carry" version of the P220, which has a shorter barrel and is slightly easier to conceal. I don't have any experience with the S&W M&P, but have a couple of Sigs and trust the brand to perform well. I realize that the Sig may cost you about $200 more, but I believe that it is worth it.
The P220 Carry has a 3.9 inch barrel and comes in several variations of trigger action and style. I personally like the traditional Sig DA/SA trigger, and would probably get that variation with stainless slide: