A significant benefit! We generally recommend that sites enforce a COOP policy of same-origin if possible. Suppose that your site, example.com is a social network. If a user receives a message from someone else, they can click on a link and it will open the link in a popup. If your site uses same-origin-allow-popups then that opened site gets a reference to your site’s window object and thus can still do many XS-Leak attacks.
We generally recommend thinking about restrict-properties as a relaxation compared to same-origin, but a reasonable one that sites can use if necessary. For example, if you have a specific page that needs to be opened in a popup, consider using restrict-properties to protect it. This provides more protections than same-origin-allow-popups and also makes it possible to achieve cross-origin isolation. The one downside to using restrict-properties is that it is currently a Chromium-only feature.
For the purposes of COOP, a popup is a new tab or a new window that is created via window.open or setting a target="foo" attribute on an anchor tag. Note that browser-created modals (like alert and confirm) and HTML modals overlaid on top of an existing page are not popups.