Persistence. If you log into a website in a container, cookies will be stored locally within the context of the container. Those cookies can't be used to track you on other sites outside the container, but they do fulfill their purpose within the container.

Primarily, it's not 'other than convenience', because that's huge.

But to actually answer: you can remember cookies etc., they're just only accessible within that container silo, versus private/incognito windows where they're deleted (by design) when you close that tab.

You can only open one private session, you can have as many containers as you want. With the caveat that you can probably spawn multiple chrome sessions each with a different profile, but then each session will have it's own bespoke config and (lack of) extensions.

I dearly wish that I was able to purge cookies/local storage on a per-container basis.