There is a certain aspect of path dependence here. Barrels and amphorae aren't just different in material, they are different in a lot of ways that have direct impact in their use. For example, to carry an amphora off a ship onto a dock you would pick it up by the handles and carry it, while a barrel would be rolled. Likewise, storing barrels and storing amphorae require different sorts of interior architecture in a ship.

Have a look at this thread. It's not exactly the same question, but I think some of the answers are relevant to yours.

Amphorae fall under the "if it ain't broke, don't fix it" rule. They are ancient technology dating back to the stone age (6000 BC or earlier). They can be made from local materials anywhere there is clay, which is nearly everywhere there were human settlements. They can be made by anyone who can make ceramics and require around the same level of local infrastructure as it takes to make bread or bricks, which is practically nothing. They can also hold almost anything, from dry goods to olive oil, wine, what-have-you.

They were dirt cheap, ubiquitous, and could be used for anything and everything.

Barrels may seem simple but they are actually vastly more complex and expensive compared to amphorae. They require wood, and not just wood but precisely cut wooden planks, and carefully bent into shape. It requires a lot more labor by specially trained makers and more resources to make a barrel compared to an amphorae.

Nevertheless, Romans did use barrels, after they learned the techniques from the Gauls, sometime around the 3rd century AD. But the added expense meant that they tended to be reserved for specific items, such as wine (which was also stored and aged in the barrels), at least initially.