It really depends on the scene in question.
By the time most images from a Digital Still Camera (DSC) make it to the internet they most likely have been cropped and downsized (or resized by the online application that displays them) to the point that there is very little discernible difference for photos taken under bright light. Where the difference becomes more noticeable is when the scene photographed presents greater challenges: High contrast/dynamic range, low light, fast action in less than ideal light, lighting with a strong color cast, etc.
In those type of situations the advantage of a larger sensor with more sensitive sensels, more options for the user to control the way the camera records the scene, and the ability to adjust individual areas of the photo independently to a much greater degree using files recorded in RAW format, rather than JPEG, should allow the DSC in the right hands to get shots the smartphone can't.