Daniel,
There are a number of reasons. Firstly, Britannic's breadth and metacentric height (crucial for stability factors) were different to Olympic; she was wider. Thus she could cope with the extra weight that these davits would bring.
As Olympic had already been built, the installation of gantry davits would not only be horribly expensive, but may well have had an adverse effect on her stability with all the extra topweight, even if she had been fine beforehand.
Furthermore, Britannic's superstructure had to be strengthened to cope with the additional weight of the davits and the concentration of weight at eight specific points, additions such as girders being installed. Olympic would have needed similar modifications, but as she had already been constructed and outfitted this would have been impractical, as well as uneconomic. Had gantry davits been fitted without modifications, not only would her stability have been in danger, but also it would be inviting structural problems within a few more years of service.
One final point is 'looks' -- Olympic was widely considered to have a beautiful profile, and gantry davits would hardly have improved it. They didn't for Britannic, but by the time she was built White Star was not only trying to outluxe the new 'Imperator' class German liners, but was trying to construct one of the safest vessels afloat.
Best,
Mark.
