We have experience with crane, garage, and dinghy on platform. None with a davit as it's really not very conducive to where we use a boat or our speeds or the size RIB we use.
We would only personally choose the platform over crane given ideal circumstances-a platform designed for that, a platform that raised and lowered a good distance, one that was very wide, and one on which the weight had been tested as to it's impact on ride and performance. Also, just lack of space for a crane and dinghy.
Otherwise crane. That boat appears well set up for a crane. As to the question regarding stability, I'd be more concerned with the impact of it adding weight off the back than on the upper deck that was designed for it.
On that boat unless a compelling reason otherwise, we'd go for a crane.
As to the comment of raising out of the water, while putting one in chocks on a platform that lowers is easy, a properly set up crane is just as easy as most davits I've seen used. Now part of that is proper lifting cradle for the RIB. Plus most cranes can handle more weight than davits.