According to HTML 5.2:
When specified on an element, [the
hiddenattribute] indicates that the element is not yet, or is no longer, directly relevant to the page’s current state, or that it is being used to declare content to be reused by other parts of the page as opposed to being directly accessed by the user.
Examples include a tab list where some panels are not exposed, or a log-in screen that goes away after a user logs in. I like to call these things “temporally relevant” i.e. they are relevant based on timing.
On the other hand, ARIA 1.1 says:
[The
aria-hiddenstate] indicates whether an element is exposed to the accessibility API.
In other words, elements with aria-hidden="true" are removed from the accessibility tree, which most assistive technology honors, and elements with aria-hidden="false" will definitely be exposed to the tree. Elements without the aria-hidden attribute are in the "undefined (default)" state, which means user agents should expose it to the tree based on its rendering. E.g. a user agent may decide to remove it if its text color matches its background color.
Now let’s compare semantics. It’s appropriate to use hidden, but not aria-hidden, for an element that is not yet “temporally relevant”, but that might become relevant in the future (in which case you would use dynamic scripts to remove the hidden attribute). Conversely, it’s appropriate to use aria-hidden, but not hidden, on an element that is always relevant, but with which you don’t want to clutter the accessibility API; such elements might include “visual flair”, like icons and/or imagery that are not essential for the user to consume.
The semantics have predictable effects in browsers/user agents. The reason I make a distinction is that user agent behavior is recommended, but not required by the specifications.
The hidden attribute should hide an element from all presentations, including printers and screen readers (assuming these devices honor the HTML specs). If you want to remove an element from the accessibility tree as well as visual media, hidden would do the trick. However, do not use hidden just because you want this effect. Ask yourself if hidden is semantically correct first (see above). If hidden is not semantically correct, but you still want to visually hide the element, you can use other techniques such as CSS.
Elements with aria-hidden="true" are not exposed to the accessibility tree, so for example, screen readers won’t announce them. This technique should be used carefully, as it will provide different experiences to different users: accessible user agents won’t announce/render them, but they are still rendered on visual agents. This can be a good thing when done correctly, but it has the potential to be abused.
Lastly, there is a difference in syntax between the two attributes.
hidden is a boolean attribute, meaning if the attribute is present it is true—regardless of whatever value it might have—and if the attribute is absent it is false. For the true case, the best practice is to either use no value at all (<div hidden>...</div>), or the empty string value (<div hidden="">...</div>). I would not recommend hidden="true" because someone reading/updating your code might infer that hidden="false" would have the opposite effect, which is simply incorrect.
aria-hidden, by contrast, is an enumerated attribute, allowing one of a finite list of values. If the aria-hidden attribute is present, its value must be either "true" or "false". If you want the "undefined (default)" state, remove the attribute altogether.
Further reading: https://github.com/chharvey/chharvey.github.io/wiki/Hidden-Content