The paper presents video quality assessment issues that include different methods. A subjective video quality assessment of the MPEG-4 / H.264 encoded clips, at the selected bitrates and picture resolutions, is shown. The authors underline the necessity of using a subjective approach to complement objective methods and propose the measurement scenario and the assessment procedure in a specially designed test environment, based on the methods presented by the International Telecommunication Union. The research shows a high correlation between results obtained while using objective and subjective quality assessment methods. The paper presents also the differences between the subjective assessment grades depending on the type of the user equipment, i.e. personal computer and mobile phone. The authors propose a statistical analysis of the results as a method of selecting significant differences between formats of video chunks that may be chosen in video transmission using adaptive streaming techniques over HTTP.