Both at once, which is how a page of a real site is usually built and the only arrangement in which either sidebar can be judged. On the left is a page sidebar: a region of the theme, outside the content, carrying a menu block with the navigation of the library in it. On the right is a layout sidebar: a region of the layout this text is laid out with, inside the content region, carrying what this page is. Three columns, two of them sidebars, and only one of them belonging to the page.
What the combination adds is that the second measurement now depends on the first. The page sidebar takes its width out of the window and hands the rest to the content region; the layout then has to place its own column in what is left, which is a good deal narrower than the window it would have measured itself against on the previous page. A layout that decides on a media query is asking the wrong element how much room it has, and it goes wrong exactly here: it keeps its two columns because the window is wide, while the content region it is actually inside has already run out of room. A layout that decides on a container query asks the element it is in, and folds when that element is too narrow no matter how wide the window is.
So the interesting widths are not the ones either example has on its own. Narrow the window slowly and there are two thresholds to cross rather than one: the width where the layout gives up its column because the content region got too narrow, and the width where the page sidebar gives up and stacks, which hands the content region its room back. If those two fall in the wrong order, there is a band of widths where the page has stacked the navigation under the content and the layout is still trying to hold two columns in it, or one where the content region is at its narrowest and both columns are still there.
The other thing to look at is the reading order once everything has stacked. There are now three columns to flatten into one, and they do not all belong to the same thing: the navigation is the site, the body and its meta column are the page. A stack that puts the page metadata above the body it describes, or the site navigation between them, reads as a jumble even when every individual block is styled correctly.
Last, the two sidebars should not look alike. Side by side they are the same shape and the same width, and what is in them is what tells them apart: on the left a menu, with a nested list and an active trail, and on the right a short run of labelled fields. A theme that gives both the same treatment is telling a visitor that navigation and page metadata are the same kind of thing. This is the page to check that on, because it is the only one where they can be compared without scrolling between two tabs.