From what I understand the MRICS is a strong up and coming designation, and the ASA is solid. Both are sponsor members of the Appraisal Foundation. Visit their websites and call their membership departments for more information. In my opinion, in the future the MAI will not be the only game in town.
"The RICS designation ( Royal Institution of Chartered Surveyors) is the most known Internationally especially in UK and other countries. They have about 120,000 members, dates back to 1885. The RICS accepts credit from approved Universities rather than offering its own courses.
I have also held the ASA designation. It is the best for business appraisers. It dates back to the 1930's."