Are these straight out of the camera JPEGs? If yes, the camera does quite a bit of onboard post processing, which can result in very different final results. If you happen to have the raw files and process both identically you'll likely get a very similar look between the two photos.
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it's tough to know what you're seeing without seeing it. can you post a side by side showing one image at 160 and another at a bigger iso where you aren't noticing this effect?
Any camera would struggle with a scene like this with bright white flowers and dark green leaves. You'd need quite wide dynamic range for proper exposure without post processing.
Usually cameras have a sweet spot ISO that gets maximum dynamic range, the fujis have a dynamic range boost setting to further complicate this but I do think the maximum natural dynamic range for the fujis is around 200-400 ISO.
Have you tried taking RAW format photos and doing a little post-processing (in particular whatever more detailed Histogram or Luminance tools you have)? This sidesteps a lot of functionality that usually guesses right, but can go horribly wrong.
Are you manually setting all three of aperture, ISO and speed? If not, double check what the auto settings of the others are (you should be getting those details in the photo meta data - visible under Properties|Details in Windows, as well as "Live").
Apologies if this question comes off as insulting, but just to confirm, if you're shooting manual, when you adjust the ISO to keep the exposure value the same right? The photo you've got there looks slightly underexposed to me
That being said, assuming you are keeping the exposure value equal, then conventional wisdom says that you get slightly less contrast (including colour contrast) with a wide open aperture. So if you set the ISO faster, and don't change your shutter speed, your aperture will be smaller, and you should be getting more colour contrast.
On top of that, each lens has its own "sweet spot" where it gives you the best image quality (sharpness, contrast, saturation etc) generally but not always somewhere around f/8.
So if you haven't already, true adjusting your ISO to 160, and getting your aperture as close to f/8 as you can, and adjust the shutter speed to achieve that.