Crop a video to 3:2, the 35mm still frame. It is the shape of most mirrorless and DSLR sensors and of a 6x4 inch print, but almost no camera records video at it.
A stills ratio applied to motion
Camera video modes output 16:9 regardless of sensor shape, so a 3:2 clip is a crop rather than a recording. That makes this the ratio to reach for when moving footage has to sit beside stills from the same shoot without a visible change of frame.
The crop is light. A 1920x1080 frame keeps 1620x1080 at 3:2, so 84% of the width survives and most compositions hold.
Print and layout
3:2 also matches standard photo print sizes and a lot of editorial layout. When a clip is destined for a poster frame, a contact sheet, or a print-derived grid, matching the surrounding stills is usually worth more than keeping the extra 300 px of width.
Keeping the full frame
Fit with bars puts the whole 1920x1080 picture 1920x1080 into a 1920x1280 frame, with 100 px of background above and below. At this ratio the bars are thin enough that black reads as an intentional border rather than a letterbox.