It all depends on your preferences. Brushed stainless steel is created when the manufacturer uses a brush at the end of the production process. The stainless steel solidifies with small brushstrokes that give it a novel appearance.
The brushstrokes serve two purposes. They create a more unique aesthetic for home cooks that don't want shiny cookware. But they also make it harder for fingerprint smudges and food spots to be visible.
Shiny stainless steel looks great at first. But as it becomes dirty, it looks annoying. Any food spots or finger smudges may quickly become distracting. You might feel compelled to regularly clean shiny stainless steel cookware. No need to worry about brushed stainless steel cookware.
In the end, both types of stainless steel are durable and anticorrosive. Which is better depends on your aesthetic preferences or how often you use the cookware.