Yes. If both images are saved at the same resolution and the lenses are otherwise comparable, the 6mm lens will show more detail on the subject than cropping the 4mm image down to the same narrower view.

Why: the 4mm lens spreads the available pixels over a wider scene. To match the 6mm framing, you would need to crop away part of the 4mm image, which leaves fewer pixels on the area you care about. Fewer pixels means less detail.

So a native 6mm view at 1920×1080 will retain more detail than taking a 4mm 1920×1080 image and cropping it to the same field of view.

The same logic still applies at full 3MP: using the longer lens directly gives more detail on that narrower area than using the wider lens and cropping afterward.