There are more than 200 boats on mooring balls where I'm currently docked, and the ONLY boats that tend to swing all over the place are those with fin keels. Those with full keels stay in place, face directly into the wind, no problems.
When I had a Catalina 27 with a fin keel, at anchor it was swinging wildly with the wind. A small stay-sail measuring just over 3 X 4 feet attached to the back stay solved the problem completely. Even during very high winds, and wild changes in the tide the boat was steady.