Slower shutter speeds will give deeper colors, but that is mostly with film. I have heard that iIt does help with digital but not like it does with film. Don't ask me why.
I've tried using normal shutter speeds and slow one's and have not noticed much difference. If you are using slower shutter speeds and your image is getting washed out, you need to adjust your aperture and ISO to compensate. For your aperture, I would keep it between f/11 and f/16 min. Any smaller than that and it will start to affect image quality with diffraction. Set your ISO to the minimum you can...usually this is ISO 100 or so.
If your image is washing out, it's because it's not a proper exposure. Just changing your shutter speed without adjusting the other legs of the exposure triangle will make your exposure incorrect.
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