>If you can expand any on why it's the hazard ratio, and not those median value differences, that really matters, I'd greatly appreciate it.<
The short answer: The p-value (for a given sample size) is very closely tied to the hazard ratio, but the p-value is not at all affected by the median values per se in the trial arms.
The longer answer: The median values are the points on the survival curves for the trial arms where the curves are intersected by a horizontal line drawn at a height of 0.50 on the y-axis. However, there is nothing magical about this 0.50 height on the y-axis—it is merely a convention. (From a mathematical standpoint, it would make just as much sense to report the values where the survival curves are intersected by a horizontal line drawn at a different height; however, everyone uses 0.50 because everyone else uses 0.50, i.e. it’s an arbitrary convention.)
The moral: If you ignore the reported median values and focus instead on the hazard ratio, you will immediately garner an edge relative to 95% of all biotech investors and professional analysts.