Hi all,
I just went through this process of decision a little while ago too! I decided on the convex ones. I realised that almost all arcade machines use concave buttons but I thought I would give the convex ones a whirl.
I am pleased that I did. Main reason, and one that no one has yet mentioned is not because they are "quicker" but because when moving from one button to another, it is easier.
I will explain - for something like a shooter where your finger(s) will be solely concerned with one button and mashing it as quickly as possible, I see no problem with the concave design. Indeed it could well be preferable as your finger is only moving up and down a very little bit so you keep in the dimple and always hit the centre of the button.
With fighting games where you are slamming buttons and moving from one to the other at great speed (though I would love a hand with six fingers!), it is more comfortable with the convex design. if you hit the edge of a dimple button you are hitting a ridge and that means that all the force of you mashing that thing is concentrated on a small part of your finger. With a concave button, you hit a much larger surface and it is therfore better for your fingers.
This, of course only really matters when you hit the button off center, but this often happens in fast and furious fighting games so I deem it rather worthwhile.
Also - it happens even more often in games (like sfa) where you have to push a whole row of buttons at once! People with smaller hands will more likely hit the middle button well but those on either side, not so well.
Anyways, that is my 2c and I hope it gives thought to anyone, who is having trouble deciding.
phill.