It is an issue of analog vs digital. When using component cables, the signal is converted to analog before going over the cables. When someone uses the HDMI socket, the signal stays in the digital domain until later in the signal path, if it gets converted at all. For example. I use an RPTV, which consists of CRT 'guns' (altho a bigger 'box', I think the color transitions, within the picture, are more natural. But this is personal preference and digital is improving in this area, all the time). This is in the analog domain. So the question is, where do I want to convert to analog? 1: are the converters better in the ps3, or in my rptv, and 2: Is it more useful to leave the signal in the digital formal until it reaches my tv? In my case, the signal goes to the switcher in my THX processor before the video portion moves on to my tv (via an HDMI to DVI cable). In this case, it is better for the signal to stay in the digital realm throughout this process, for a few reasons that I won't bore you with here. If you are using a setup which allows the signal to remain in the digital domain though the entire process, why convert to analog, then convert back to digital at the tv? In some cases, this might be necessary because of limitations in your gear. However, if the beginning, and ending formats are digital, and you want the best quality result, it is best to keep the information as pure as possible, without the digital 'noise' that converters can add. Also, there is one more issue to consider. When using a component cable, only the video portion of the signal gets transmitted, necessitating the use of a separate cable to carry the audio. HDMI carries both audio and video. This means less cabling. I hope this helps.
Also, occasionalracer is correct. If you are willing to spend the money to purchase higher quality component cables, the differences will still be there, but they will be narrower. For those with limited budgets, check out bluejean cables:
http://www.bluejeanscable.com/