In a large bowl, combine cream cheese, mozzarella cheese, green onions, Worcestershire sauce, soy sauce, garlic, sugar, and crab meat. Set aside.
Preheat a medium non-stick skillet over medium-high heat.
Butter one side of each slice of bread.
Place one slice of bread, butter-side down, into the skillet. Top the slice of bread with about ¼ cup of crab mixture, spreading it evenly over the bread. Top with a second slice of bread, butter-side up.
Reduce heat to medium-low. Cook for 3-4 minutes. Then, flip over the sandwich and cook another 3-4 minutes, or until golden brown. (If it seems like the bread is taking a long time to brown, be patient, as the cheese inside needs time to melt.) Use a spatula to remove from the skillet.
Repeat for remaining sandwiches. Serve with sweet chili sauce or garlic chili oil for dipping (optional).