Ang and Goh (2010) administered a survey to 396 children aged 12-18, measuring their affective and cognitive empathy levels as well as their self-reporting on what cyberbullying they had participated in and how frequently they had participated in such behavior, and breaking it down by assigned gender. (note: Affective empathy is emotional: the ability to feel what others feel. Cognitive empathy is mental: the ability to understand the emotions of others.)
They found that when children don't have much affective or cognitive empathy, they're more likely to bully (obviously) and that this is the same regardless of gender. High scores of affective empathy made girls less likely to cyberbully even if their cognitive scores were low, but this was not true for boys. This could be due in part to the fact that overall, girls scored higher on both forms of empathy, so maybe 'high' affective scores for boys were not high enough to prevent bullying: the 'high' affective empathy for boys was significantly lower than the 'high' affective empathy for girls. Or it could be partly due to the fact that girls are trained to make moral decisions based on emotion (avoidance of guilt), whereas boys are trained to make moral decisions based on thought (avoidance of judgement); thus, affective empathy has a stronger effect on girls than it does on boys, because it is actively brought in to the decision-making process.
Regardless, the fact that cognitive empathy is the only form of empathy to reliably prevent cyberbullying across gender means that cognitive empathy is important to teach to children, particularly in online environments.
[reference]Ang, R. P., and D. H. Goh. 2010. "< a href="http://link.springer.com/article/10.1007%2Fs10578-010-0176-3" alt="http://link.springer.com/article/10.1007%2Fs10578-010-0176-3">Cyberbullying Among Adolescents: The Role of Affective and Cognitive Empathy, and Gender</a>." Child Psychiatry & Human Development 41, no 4: 387–397. doi: 10.1007/s10578-010-0176-3