In general concave buttons are significantly longer travel than convex, which does inherently mean less responsive.
Button shape!=travel distance.
OK, I will be more obvious this time ...
What would be more useful to people trying to choose amongst buttons is a statement like "Sanwa buttons/switches are more responsive that Happs concave buttons/switches".
If I am not being clear, consider the fact that Happs convex buttons and Happs concave buttons use the same switches and have pretty much the same travel distance (at least according to the buttons in my box o' buttons).
The actual shape of the button top is irrelevant to the travel distance or switch responsiveness (it is like saying that ball handles are more responsive than bat handles).
And, as I tried to point out, generalized statements about travel don't necessarily apply to tuned leafswitches.
FWIW, for twitchy fighter stuff, I would use Sanwas ... but I am one of those oldtimers who is "trying" (

) to recreate an experience, although I really like my Galaga and Asteroids fire buttons to be hair trigger.