He did it: Redbull Stratos jump!

So here we have two speed profiles, one is my limit case linear equation. The other is a case where drag force is considered, no real numbers of course.
I think you can agree with me that the downwards acceleration decreases as our friend Felix's speed increases, so the slope of the speed vs time curve should too. With that we'll always have a curve that starts out with a greater slope and ends with a smaller one, like the one in my example above.

With that it's easy to see that the curves considering the drag force will ALWAYS have an average that's closer to its maximum when compared to the linear profile.

Now, here I'm not actually considering what the real max speed he'd reach if there was no friction or calculating the effect of the drag force. What I'm doing is applying these theoretical profiles to the numbers we can trust in his story: the distance he fell and the time he took, which, together, get us his average speed during fall.
So if for both of the cases shown in the graphs Vavg has the same value, it should be obvious that Vmax for any case with the drag force taken into account will always be smaller than that of the linear one.