In recent years, the proliferation of multimedia applications and formats, such as IPTV, Virtual Reality (VR, 360-degree), and point cloud videos, has presented new challenges to the video compression research community. Simultaneously, there has been a growing demand from users for higher resolutions and improved visual quality. To further enhance coding efficiency, a new video coding standard, Versatile Video Coding (VVC), was introduced in July 2020. This paper conducts a comprehensive analysis of coding performance and complexity for the latest VVC standard in comparison to its predecessor, High Efficiency Video Coding (HEVC). The study employs a diverse set of test sequences, covering both High Definition (HD) and Ultra High Definition (UHD) resolutions, and spans a wide range of bit-rates. These sequences are encoded using the reference software encoders of HEVC (HM) and VVC (VTM). The results consistently demonstrate that VVC outperforms HEVC, achieving bit-rate savings of up to 40% on the subjective quality scale, particularly at realistic bit-rates and quality levels. Objective quality metrics, including PSNR, SSIM, and VMAF, support these findings, revealing bit-rate savings ranging from 31% to 40%, depending on the video content, spatial resolution, and the selected quality metric. However, these improvements in coding efficiency come at the cost of significantly increased computational complexity. On average, our results indicate that the VVC decoding process is 1.5 times more complex, while the encoding process becomes at least eight times more complex than that of the HEVC reference encoder. Our simultaneous profiling of the two standards sheds light on the primary evolutionary differences between them and highlights the specific stages responsible for the observed increase in complexity.