Current images from color RC papers are expected to last from 100 to 200 years depending on the keeping conditions and manufacturer. This has been achieved during the last 10 years or so, although overall image stability has been improving constantly for the last 50 - 60 years since the introduction of the first color imaging materials.
This would probably not be possible on Baryta paper support. It is mainly due to the UV absorption properties of Baryta vs Titanium Dioxide used in the two products, but also in other factors involved in the RC/TiO2 base. For example, it is possible to incorporate antioxidants into RC support for stability that are impossible to add to Baryta.
OTOH, B&W images in silver are apparently of similar stability on either Baryta paper or RC support and are limited mostly by the quality of the process and the stability of the paper. At the present time, Baryta paper images are known to survive for over 100 years.
Early RC prints are not as stable due to the degradation of early RC due to UV and oxygen.
Having been directly involved in the testing of these images from about 1965 - 1970, and having kept up with the studies thereafter, I am quite aware of the advantages and disadvantages of the paper, dyes and silver images.
I might add that at normal viewing distance, you might not be able to distinguish between a color print on baryta support and a color RC print.