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The area of the contact patch at the same pressure remains the same, whatever the size of the tire. In other words, traction and handling should be unaffected... all else being equal... of course, sidewall stiffness is a much bigger issue with a narrower tire... and narrow tires don't come with the nice sticky rubber you can buy with wider performance tires, but if you're getting the same exact tire model in different widths, the only thing working against the narrower one is the flex in the sidewalls.
What changes there are are in the shape. Narrow and small are not ideal because the shape is long instead of wide. This means more flexion of the tire and more heat build-up, with less tire to absorb it... which is not ideal.
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