There is growing evidence that virtual reality (VR) can be used as an optional therapy method for stress relief and treatment of mental disorders such as a variety of anxiety disorders, depression and psychosis. However, more systematic studies to quantify the effects of VR for emotion elicitation and compare the effects of 3D and 2D environment for the same is necessary to design feasible and effective treatments. In this study, we design a cross-over experiment protocol comprising of two emotion eliciting environments relaxation and arousal - that is presented to the participant either in a 2D monitor or a 3D head-mounted (HMD) VR display. The EEG data is collected during the experiment and analyzed offline to classify emotion elicited by low and high arousal environments using SVM classification of band power features. A 10-fold cross validation is performed and classification accuracy for each subject is computed for 3D-VR and 2D-screen display. The average classification accuracies over subjects are obtained as 66.88% and 59.27% in 3D-VR and 2D-screen group respectively. The performance difference between 3D-VR and 2D screen is statistically significant (p < 0.05), indicating that 3D-VR generates more distinct EEG patterns associated with emotion elicitation. Further, significant differences in band powers from alpha, theta and beta bands are also observed between both groups. The results presented in this paper support the use of VR as an effective tool to study emotion elicitation and regulation, compared to a 2D screen.