This is really sort of an interesting question. There are certainly some reasonable "wants" in here -- fast reaction, low noise, and so on. Any of the cameras you indicated (as well as the ones pointed out by others) are going to be an improvement over your S3IS, but I think it's also important to understand that you, as an artist, are part of the process here.
Let me explain. As a photographer, you're really painting with light on the sensor of the camera, and the camera gives you features that help with that. Any camera is going to have a sensor of some sort. It's going to use aperture and shutter speed to control how much light gets to the sensor, and it's going to use ISO to make the sensor effectively more or less sensitive to the light that's hitting it.
More expensive cameras have a larger envelope of capabilities (larger / better sensors, higher ISO support with less noise, etc.), and they're generally going to have features that make "automatic" stuff easier or better. A higher-end camera, for instance, might sample more points for autofocus or exposure calculations, which will help it perform these functions better and faster. In that respect, a Canon 5D set on 'auto', will take better pictures than your S3IS on 'auto', all things being equal, because it's got a vastly larger performance envelope and the smarts to know how to use it.
But I'd argue that to look only at the capabilities of the camera is to leave out an awful lot of the "art" of photography. "Capturing a moment without any thought" is an admirable goal, but you probably need to reflect a little on what it is about the moment that you're trying to capture, exactly. I mean, are you capturing this for you, or for someone else? What is it about the moment that you find worthy of picking up your camera in the first place? What, exactly, are you trying to get someone to see in your photo?
In addition to composition, I think you may find that there's a lot of artistic potential in post-processing, too -- especially if you start shooting RAW (which any of these DSLR's can do). You'll end up with a lot of control over white balance and color, as well as noise levels, contrast, sharpness, and so on. Chances are, you'll see better results with a cheaper camera and good post-processing than a (slightly) more expensive camera with no post-processing.
Maybe I'm reading way too much into your question in terms of the non-camera stuff, but as an artist, I think you should be able to appreciate the idea that a great artist is going to be more likely to produce great art with marginal equipment than the other way around.