Both Botox and Dysport are forms of botulinum toxins and basically do the same thing. However, Dysport has fewer proteins surrounding the main molecule, which allows it to be tolerated by the body to a greater extent than Botox. Also this slight structural difference causes it to be broken down at a much slower rate. However results vary with individual physiology. So if Botox does not give the results that the patient wants, Dysport should be considered. And likewise, Botox should be considered if Dysport does not deliver ideal outcomes.
There is a study which compared the effects of Botox versus Dysport on crows feet. The subjects had Botox injected on one side of the face and Dysport on the other side. According to the results, Dysport outperformed Botox in the overall reduction of crows feet.
One patient complained about the lines between his eyebrows. He had used Botox in the past, but did not get the kind of results he wanted in this particular area. His wife also had the same issue. Both of them had Dysport injected on the same day and noted that the results much faster. They were also impressed by the efficacy of Dysport on this glabellar region. Here is a video where the patient describes this.