A few things we know for sure: European butter is more expensive than other store-bought butters. It also tastes incredible on a baguette and often has a deep yellow color and can be crumbly and dense. But do any of these things actually mean anything when you're baking?
Cultured or European-style butter (as it's often called) is made more slowly than other store-bought butters so the cream has time to develop in flavor. The main difference between these European-style butters and all of the rest is the fat content: they have a 83-86% fat content while non-cultured butters hover right around 81%. And butter with less fat contains more water which can literally act as a binding agent gluing down layers of dough and, all the while, creating a tougher pastry.
So science aside: if you're making simple cookies or brownies, I wouldn't splurge on European-style butter. But if you're making pastry or laminated dough that will have layers (croissants or pie dough, for example), European-style butter will make a big difference. Because it has less water it'll remain solid for a longer period of time in the oven, resulting in many more layers. When baking pies at home, I love using Kerrygold Pure Irish Butter. If your Trader Joes is anything like mine here in California, you can find it for a reasonable price . You'll notice the difference in your pie crusts right away: Guaranteed.
Related: So Delicious! Kerrygold Irish Butter