I don't see a whole lot of difference.
I have the Fuji S9100
According to reviews there isn't a whole lot of difference between
the fine setting on Jpeg and RAW.
RAW also slows the camera down a lot.
So why would I bother?
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In god we trust, all others are suspects
I don't see much difference either, when I download the photos to my computer. If I do see a difference it's that the jpegs are sometimes better. This is because if the camera is set on jpeg, the camera takes the raw image, applies a white balance filter, may perform some noise removal, sharpens it (even if your sharpening is set at zero) and applies any further processing you have set the camera to perform and then it compresses this raw file into a jpeg file.
So a jpeg is already processed. Further processing (with good quality results) can be difficult because a lot of the original information in the raw image is no longer there. You can make adjustments but extensive ones will lead to artifacts and other types of image degradation.
The raw photo however has had nothing done to it. It's te original unprocessed file. All the information is still there to easily change white balance to anything you want. You can easily adjust exposure evenly across the entire image at least 1 stop (even 2 stops) in either direction. (although blown highlights or clipped shadows can't be fixed) After these corrections are performed (if needed) further processing can be done with far better results than what you would get trying to do the same processing to a jpeg. Being able to choose, say the method of sharpening, depending on the particular photo can really help to get the best final results for viewing.
Nothing wrong with jpegs. But you're limited to the processing available by the camera and while some adjustments can still be made to a jpeg, it's pretty much meant to be a final result to which only very minor further processing can be done. With raw, all the processing is completely your choice. And very powerful programs (compared to what's in the camera) can be used to process the photo to a person's own taste which may differ from what the camera can give you no matter how much you mess around with it's controls.
Some people like the idea of being able to make all the choices in the processing of their images. No different than some people used to like working on their photos in the darkroom.
Like film, you could send your negatives to the photomat to have them processed and you're stuck with whatever comes out of the machine, much like you are when taking jpegs with digital. Those who like to take control and develop their negative to their own specifications could do so by developing them in the darkroom. Neither way is better than the other but simply depends on the photographers choice.
Raw vs jpeg isn't a matter of what's better out of the camera but what you can do with it after it comes out of the camera.
Using raw can seem like a pain in the butt sometimes, expecially with a digicam. But personally, having limited choices in the processing of my photos would be a pain in the butt too. But, like anything, a person should choose what's right for them. I can't see myself limiting the processing of my landscapes to only what's available from my camera. I'm quite picky about this. Quite serious, in fact. OTOH, if I'm out doing bird photos using sequental shooting, using jpeg is just fantastic compared to raw. Trying to do it with raw would really ruin my fun. So it depends what a person wants. Overall, using raw isn't better than using jpegs, IMO. What's better is simply having the choice.