Styling the second sidebar

Per the register_sidebars() Codex page, the CSS ID of the sidebars gets incremented by default. In other words, if you’re not explicitly setting the id array value — and in your code sample above, you aren’t — you would end up with sidebars with CSS IDs of sidebar and sidebar-2. You can then style them differently in your CSS file (be it style.css or a custom one that you’ve added):

#sidebar {
    /* Styles */
}

#sidebar-2 {
    /* Styles for the 2nd sidebar */
}