Hello there, thanks for visiting our forums.
The best advice I can give you is to check the results page of our review of the S9500 where you'll see it compared against the 350D with its bundled 18-55mm lens. There's also a discussion about the 9500 versus an SLR in the verdict.
Just briefly though, the main differences in the favour of the 350D are lower noise, higher sensitivity, quicker general response, easier manual focussing and of course the ability to change the lens.
In the 9500's favour over the 350D, you've got a much longer lens zoom range, better macro performance, a movie mode, composition with the screen and no chance of getting dust on the sensor.
If you like the convenience of having an all-in-one camera with a long zoom range and a movie mode, then stick with the 9500. If you want to get into more advanced or specialist photography, such as using high sensitivities or swapping lenses, then an SLR will be more flexible - and the 350D is a great choice.
Hope that's helped, although for a greater discussion of the pros and cons, check out our review of the S9500.