Generally speaking, my experience as a young guy and now an old geezer paddling with 2 daughters agrees with your analysis. I think girls generally are as or more competitive than guys but it can be expressed in other ways.
As another oversimplification about why people paddle:
(young) guys: it's fun and if I survive a harder river than you then I'm better.
gals: it's fun and , well honestly, if I show up some guys it's even more fun.
as for an old(er) guy, well, I'm having loads more fun now on the river with my daughters than I did in 1980 with my buddies.