Okay, let's see what we've got here.
First off, both cameras selected the same basic exposure: 1/60, f/4, ISO 400. And the basic exposure worked the same, as evidenced by the brightness of the image on the TV set in both pictures (that won't be affected by the flash).
So the difference is strictly in the flash.
The DReb/300D and XT/350D use different flash metering systems. The DR/300D uses E-TTL, while the XT/350D uses E-TTL II. Both use an "evaluative" approach to metering the flash, but they have very different ways of determining what it is that you're trying to take a picture of - and therefore what needs to be lit up correctly by the flash.
A short detour: this scene has a wide range of distances involved, from the black thing that sticks out from the lower right to where the walls meet in the far corner. But the amount of light that an object gets from the flash depends on how far away it is from the flash. The nearby stuff will get a LOT more light from the flash than the far-away stuff. Now back to the original topic... how the two cameras meter the flash.
Both cameras do flash metering by firing a low-power "pre-flash" when you press the shutter button, and seeing what happens on the metering sensors. On the 300D, the camera assumes that what you're trying to take a picture of is located at the AF sensor(s) that locked, and adjusts its flash power accordingly. I can't tell which AF sensor(s) locked on the 300D picture, but unless it was the bottom one, the camera is going to guess that your subject is toward the far side of the room. That area wouldn't have brightened very much, so the 300D is going to have to pour a fair amount of power into the flash to get that area properly exposed.
On the 350D, the camera's flash metering doesn't pay attention to the AF system at all. Instead, to figure out what you're trying to take a picture of it uses what I call the "Goldilocks" approach. It looks at each of the 35 sensors. Those that didn't brighten up very much are considered to be background, out of range of the flash (they could also be lights, like the lamp bulb and the TV). Those that brightened up too much are considered to be reflections of the flash from glass, mirrors, etc. The camera mostly (maybe totally, I don't know) ignores those sensors and pays attention to the ones that brightened up a medium amount from the pre-flash. In general, that will be the closest item(s) of significant size. In this case, that's the black thing at the bottom of the picture, the end table, and the back of the couch. Those are close to the camera and don't need much flash power to get properly exposed.
Now go back at look at the picture from the 300D. The white throw that is draped over the back of the couch is blown out, as is the white ceramic sitting on the endtable. But in the picture from the 350D, they're well-exposed.
It's just a matter of the cameras having different ideas of what you were trying to take a picture of. The 300D thought you wanted a picture of the far wall, the 350D thought you wanted a picture of the couch.
So what do you do?
Well, you could learn to work with the way that E-TTL II does its exposure determinations. Zooming in on your intended subject would help. Or if you wanted the wide angle picture, zoom in, do a Flash Exposure Lock (FEL, manual page 99), zoom back out and take the picture. If you're doing a lot of these pictures where there are large objects that are significantly closer than your intended subject is, though, you may find that all to be a hassle.
You could try one of the lenses that provide focus-distance feedback to the E-TTL II system. Supposedly, the camera takes that into account and might increase the flash power to assure proper coverage at the subject.
Or you can just shut off the evaluative flash metering entirely, by setting Custom Function 8 to 1 (manual page 150).
