What's the best answer to this?
An analogy might be comparing foods among different people. HDMI and component are simply two different ways of dealing with signaling and different displays and different components will handle HDMI vs. component completely differently. Kind of like the way different people like different foods, and the foods themselves could be different at different times.
So you get all your flavors of HDMI and all the resolutions you can send across it, and then then source needs to get that resolution out onto the cable properly, then the display has to accept that resolution and deal with it properly.
Not only is this something that was basically impossible ten years ago, but it's a feat of near magic that most displays do so well with it. So, unfortunately, depending on your source, your display, and to some smaller extent, your cable, you could end up with a better image via component then you do with HDMI. Then you could replace that display with a new one, or switch to a different source, and the HDMI cable could show marked improvement... or it may simply look identical.