A chain is only as strong as it's weakest link.
The technical truth in this age old debate has a lot to do with your size and quality monitor and the condition of your vision.
Generally speaking, assuming you have excellent vision, the difference between HDMI and Component is equal on smaller 50" or less monitors. Once you go larger in size and are feeding the monitor with a true high quality image such as a Blu Ray 1080p x 1920 image, it becomes more and more obvious you'll need HDMI or DVI connection to see all that the image has to offer. The colors are purer, the edge definition of the individual pixel is sharper. As you expand the size of the pixel with larger screens this becomes obvious assuming your vision is perfect.
The technical problem with analog cabling is that the horizontal and vertical sync is combined with the color and luminance in the green (Y) portion of the signal. This causes a bit of intermodulation distortion and corruption of the color and luminance of the pixel. The visual effect is that of a sharp pure colored rectangle pixel becomes a spot with wavy edges. Then when this pixel gets displayed on a digital monitor the pixel becomes a bit more muddy and lacks a degree of definition. To maintain digital all the way through and never see an analog translation will yield the purest transfer of the video signal possible, avoiding all the noise and distortion of the original image that can infect it on the analog side of things.
Also, on the source side of things, if that source is not of high quality to begin with, such as a SD TV image, then once again even with a larger screen the advantages of HDMI over component will be lost.
If you want to evaluate, an A-B test, of component vs. HDMI, then you need to start with the highest quality source you will work with. If it is an SD channel then don't expect to see a different. If it is an HD channel then maybe you'll see a difference on larger than 50" screens. If it is Blue Ray, then you better be using HDMI as the component difference will be obvious.
I think the bottom line is this- What will work as good enough for your system is what counts. But don't feel that if another person says I can't see a difference between Component and HDMI that will be the same for you