Answer
Concave barrel ends (bending inward) are better at storing wine.
Work Step by Step
The pressure of the wine against the barrel ends compresses the components and holds the boards together, strengthening it and helping to stop leaks. This is analogous to the compression on an arch.
You will notice that the bottoms of some wine bottles are shaped this way. Not only does it allow the bottle to stand upright (because a convex bottom would be unstable), but the bottle appears to hold more wine than it actually does, which is a win for the wine producer!
This is discussed on page 234.
