The video selection for Country Grid and Kid Grid was the same as the PC versions (author: I'm working on getting these).
Vid Grid initially had a kiddy mode with a 2x2 board and the option to play pieces in black and white which were in the wrong place (except Red Hot Chili Peppers, which was tinted blue since it was already B&W). Other play modes were one where you'd cycle rows and columns rather than moving pieces one at a time, one with pulling all the pieces from a pile and putting the video together starting with a blank board, and a few that died before they got off the drawing board as Atari had already insisted on leaving the game unchanged. Instead of the mouse, you had a gliding selection box which let you merely tap up, right right to go up one square and two over, for example. It still looked smooth, as the selector would glide about quickly. It made for much faster play.
There was also a full-screen viewing mode (the movies were encoded at a higher resolution than you see when playing), which let you cycle the videos, or pick a subset to cycle. This was nice for showing off the Jag. Lastly, although we were using the Atari-supplied video CODEC (QuickTime), High Voltage was initially using their own audio compression format which they felt yielded much better sound, but for reasons I won't speculate on here, they were forced to change back to a rather rudimentary and -very- lossy format.
Both Country Grid and Kid Grid were completed but not released.
(Email conversation with Jaguar programmer, name withheld by request)