You don't have customizable buttons with the 300D, and no flash compensation. Also, no second curtain flash, which means on a long exposure, when firing the flash, it will only fire at the beginning of the shot, (first curtain), as opposed to the end (second curtain). On the 10D you have both. I'm not a fan of flash photography myself. I hardly use it.
Your metering is limited when you are in the creative modes. If you shoot in Manual mode, you are stuck with center weighted average metering, but I find that's it's no problem, once you get used to the meter.
You get a few more frames per second on the 10D, as well as a larger buffer. Do you forsee yourself shooting lots of pics real fast, like sports photography? The 300D has a 4 shot buffer vs 9 on the 10D.
The 10D has a magnesium alloy body, for sturdier construction, vs a plastic body on the 300D, but let me tell you, the 300D is not a toy. It is plenty sturdy.
After all that, I can cite one advantage that the 300D has over the 10D, besides price. The EFS 18-55mm lens, which is only available for the 300D, which gives you a true wide angle lens, (the kit lens) for only $100. You have a 1.6x Field of View crop, because the image sensor in the camera is 1.6x smaller than a 35mm negative. So you have to multiply the focal lengths of all your lenses by 1.6. This means that your normal 28-80mm wide angle tele lens is a 44.8 - 128mm, not so wide angle. The 18-55mm lens gives you a 28-88mm lens on the 300D. It's not the greatest lens canon makes, (does suffer from barrel distortion, which is easily corrected in PS though), it is a pretty sharp lens for $100, and your best alternative for a cheap wide angle zoom.
I hope that made sense. That was a mouthfull.
