Which one are you saying is grainier? The 16:9 one uses a wider part of the film frame, so it's "zoomed out" effectively. And I wouldn't use the 4:3 version as any sort of image quality test, since it's a conversion from the NTSC version...
Grainer than other episodes in the season. Not as compared to the screencaps from a domestic source obviously. 1990s era video recording equipment tends to lose information and that's what would've still been in operation, when I taped that off British satellite channel, Sky One in 2002. That likely accounts for missing frame at the sides, probably present on broadcast. But nevertheless, even having said that, there is evidence of more above and below the widescreen frame.
If you cropped a remastered TNG episode to fill the 16:9 screen, as happened with "Broken Bow", in order to fill the frame... the grain would be enlarged, along with everything else inside the area being zoomed into.
4:3 would involve zooming out to show the whole frame, in this particular case.