Cybersickness is a symptom of dizziness that occurs while experiencing Virtual Reality (VR) technology and it is presumed to occur mainly by crosstalk between the sensory and cognitive systems. However, since the sensory and cognitive systems cannot be measured objectively, it is difficult to measure cybersickness. Therefore, methodologies for measuring cybersickness have been studied in various ways. Traditional studies have collected answers to questionnaires or analyzed EEG data using machine learning algorithms. However, the system relying on the questionnaires lacks objectivity, and it is difficult to obtain highly accurate measurements with the machine learning algorithms in previous studies. In this work, we apply and compare Deep Neural Network (DNN) and Convolutional Neural Network (CNN) deep learning algorithms for objective cybersickness measurement from EEG data. We also propose a data preprocessing for learning and signal quality weights allowing us to achieve high performance while learning EEG data with the deep learning algorithms. Besides, we analyze video characteristics where cybersickness occurs by examining the 360 video stream segments causing cybersickness in the experiments. Finally, we draw common patterns that cause cybersickness.