I have done both before. Generally I go the full route for the tank, put in stabilizer, run the bike for 5 minutes or so to get stabilized gas everywhere, then shut off the petcock and run the carbs dry (if possible). The first tank in the spring is generally not an all out ride, so the old and slightly stale gas isn't a big deal. When you get nice January days, the bike is ready for you too. I have done empty and no rust formed, but full seems safer for the tank (and any fire risk).
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