I'd rather make a notice a `<section>` with a heading, or an `<aside>` if it's not related to the surrounding content.
You could even add a more specific ARIA (or DPUB-ARIA) role like `role="note"`, `role="doc-pullquote"`, `role="doc-tip"`, etc. But don't use them unless you have multiple kinds of `aside` elements and need to help people skim.
Most of these roles actually map to the `section` superclass rather than the `complementary` role of `aside`, which isn't always a problem: the `aside` element tells reader-mode implementations to remove the element, but the `role` tells assistive technologies more useful information. I use a similar hack for my in-page section permalinks.
If the notice is important to the surrounding content and reader-mode shouldn't remove it, use a `section`.
