A good HTPC has better processing capability, and can decode videos in higher quality if configured properly. PC video controls are almost always better than consumer level media tanks. This allows you to calibrate the output more precisely. If the PC is capable enough, post-processing can also be applied on the video in real time, in case you'd like to enhance the content. Lastly, PCs are easily expandable in terms of software, storage, and processing capability.
The only major downsides are cost (initial investment and running costs are higher), convenience (bootup time, shutdown time, ergonomics, etc.) and form factor (PCs are usually larger). Other items like operating noise can easily be addressed with a well-planned build.