The issues you have to deal with on December 25 are:
1. Your incoming airline may change its flight schedule between now and January.
2. Your incoming flight may be late.
3. You have to clear customs, which could take as little as fifteen minutes or as long as an hour depending on the number of incoming planes and staffing levels.
4. It is Christmas day, so there may be a shortage of taxi drivers.
5. You need half an hour or more to get from one airport to the other. (It is a small island, but the road network cannot handle the traffic volume.)
6. Air Antillies cuts off checkin half an hour prior to flight at the Grand Case airport.
Given your flight time out of SFG, I assume your destination is Martinique. There is an Air Caribees flight that leaves later in the afternoon that would be a safer bet. Or consider flying through Miami rather than via SXM.
It the other direction going home you would not have to go through customs in Grand Case, but check-in cutoff will be between 45 and 60 minutes depending on the airline.