On average, which of these two commonly used drugs, ivermectin or hydroxychloroquine, would be more effective in reversing dementia in patients?

These each have beneficial effects and whether one would be superior to the other would depend on the individual case and the reasons behind the impairment, specifically. Not just what kind of virus might be involved but the status of the patient's immune system, their karmic history, and other factors of individual chemical makeup and genetic complement that will not be known in detail so as to make a wise choice. From the data available through scientific studies, ivermectin is in the lead with regard to supportive evidence of a benefit for viral illnesses and their consequences. But that is a function of the level of research effort, not necessarily what the potentials are. We would not want to discourage further study of hydroxychloroquine for such applications. There are situations where using the two together or in sequence would give superior results. So to make one the champion will inevitably bias against use of the other, and that would be unwise.