Analog vs. Digital
An AV component cable carries an analog signal across copper wire, while an HDMI cable carries a digital signal. This means that an AV cable is more susceptible to problems with noise, or degradation of the image. If your AV cable is especially long, the signal will degrade by the time it reaches the television. HDMI does not have this problem, because digital is essentially an all-or-nothing signal, meaning you either see a full-quality image or nothing at all.
Resolution
Both AV component and HDMI cables can convey HD signals, though they do so differently. AV component cables can handle both 720p, or progressive scan resolution, or 1080i interlaced HD. Most TVs, however, are set up with progressive scan and are not interlaced. An HDMI cable can support 1080p for televisions that require progressive resolution. If your TV supports 1080i, it would be best to test both cables to discern which is of higher quality.
Sound
One of the main advantages of an HDMI cable is that it can deliver sound and image on the same cable, reducing the need for the extra cables that AV components require. For a standard AV component cable, five cables will actually be needed. Three of these cables will carry the image signal and two of these will carry the sound signal. An HDMI cable reduces the need for an excessive amount of cables to be connected to your PlayStation 3.
Avaliability
HDMI inputs are only recently becoming popular options for HD televisions. Many models do not have HDMI, and older models will almost certainly not. Therefore, an AV component cable may be your only option for an HD signal. Most televisions will at least support 480p, which an AV component cable can convey. Also, since an AV component cable is analog, it can be converted to other inputs, for instance, if your television does not support HD.