In the US, 1.2% of children under 18 experience abuse (American Humane Association) and 77% of students experience bullying (bullyingstatistics.org). Abuse victims have entire organizations to advocate for their safety and well-being, while in 85% of bullying cases, no one intervenes (bullyingstatistics.org). But this makes sense because abuse is so much worse than bullying right? New research has found that the lasting effects of bullying may actually be worse than those of abuse.
Maltreatment was tracked until age 9 and then children were asked about bullying at ages 8, 10, and 13 and then mental health outcomes including anxiety, depression, and suicidal tendencies were assessed in early adulthood. Surprisingly, the results showed that bullying or bullying and maltreatment both increased the risk of mental health problems more than maltreatment alone. In fact, bullied participants were 4.9 times more likely than maltreated participants to develop an anxiety disorder.
If these outcomes are as dramatic as they are reported to be, the contribution bullying makes to mental illness cannot be ignored. Although the public has come a long way from thinking bullying is a harmless part of growing up, this research suggests that we need to be taking bullying even more seriously than we already are.
http://www.iflscience.com/brain/price-bullying-measured
http://www.bullyingstatistics.org/content/school-bullying-statistics.html
On Psychology and Neuroscience 
While it is true there are similar consequences, the mechanics of bullying and childhood abuse (by the parents I presume) are quite different. Without citing research I can hypothesize that bullying is usually a longer lasting phenomenon, tends to happen later in development, near adolescence and afterwards, and results primarily in social stress (sense of unbelonging and self identity). By contrast, childhood abuse would be more localized to early development, and would cause more personal stress (self-confidence, sense of self-worth and safety). In another generalization, bullying, when any sort of preventative institution is instated or even if the victim can find a confidant, can be easily partially alleviated, whereas abuse treatment has focused much more on remedy rather than prevention as there are few measures short of legal action that can prevent abuse and its psychological consequences. All in all, to understand the interaction and comparison between these two phenomena would require much more than simply analyzing the overall instances of psychological disorders in victims of each group. A more direct and accurate approach will have to incorporate the specific psychological mechanisms that each system induces and study how those particular ticks are propagated during development and sustained through adulthood.
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