It really depends how both are implemented on your display (and video source for that matter). If you have a CRT, component may be a bit better. On a digital display, more likely HDMI.
Main thing you lose in almost all cases is the ability to upconvert SD DVD's.
HDMI also gives you advanced audio options that the RCA audio or digital audio may lack though if you have 5.1/7.1 analog outs it can offset that issue
In most other cases of which looks better HDMI or Component, I have found little way to predict other than trial and error. The Rule of Thum of HDMI looks better on Digital sets and Component is better on CRT is a very spotty from what I've seen.
Like Dave H said, it comes down to how HDMI is implemented in the player and display. Theoretically, HDMI will give you a better picture because you avoid the digital-to-analog and back again conversions with component. See if you can find reviews of the player and display where they comment on HDMI vs component video quality. For example, Secrets always tests this for DVD players.
I also can not run hdmi. Tv and receiver both do not have it. I am going to run a hmdi->dvi from my player to the tv. How does this rate vs. hmdi or component?
DVI is pretty much just the video portion of HDMI. Theoretically similar, should be better than component, depending on implementation. Be aware that some players' HDMI output doesn't get converted to DVI properly though: