Tiny-III is the newer generation product (3rd generation) and has a few more features available on it as compared to Tiny-II. 1) Tiny-III specifies a parameter called I^2F which is a power co-efficient and since it is more tightly controlled as compared to Tiny-II it can reduce the overload power 2) Tiny-III has a feature called on time extension which can increase hold up time for a given input cap size. 3) Current limit is programmable using a capacitor between BP/M pin and Source pin. for the power level you are looking at this may not be applicable for you. Although its a 8 pin DIP package - Tiny-III does have a different pin allocation as compared to Tiny-II (not pin to pin compatible)

Should I switch to Tiny-III for my design, according to PIExpert? Thanks.

If it is new design then yes I would say TNY-III is the better option.

i wud suggest that try tny2. Coz if you are looking for adaptor application...TNY2 is the latest release that satisfy the application requirement with less component count, tatal cost & weight.