Any differences are going to be due to the scaling algorithms used by the browsers - which you can't really do anything about unfortunately, apart from serving the correct size image and not scaling.
Browsers have gotten considerably better in scaling in recent years. It wasn't that long ago that browsers only did pixel-resizing and the results were not very good at all.
To be honest, I don't think your screenshot is particularly conclusive - the Safari pic is only slightly "less sharp" IMO, which users are unlikely to notice - since they are not seeing a side-by-side comparison. And users of Safari are perhaps used to images appearing slightly fuzzed if it is doing that with all scaled images. Plus the fact that most users generally do not notice the finer details - unless your site is targeting other designers? What I notice more from your screenshot are the JPEG artifacts, that affects both the left and right screenshots - but this is perhaps just an issue with the compressed JPEG (or imgur)?