First and foremost, the Nintendo 64 was the best multiplayer system of the time. And while the system couldn't hope to compete capacity wise (largest cart was 512 megabits) to the Playstation, the games in general looked a whole lot better because the N64 had the power to do perspective corrected rendered polygons. The PS1 doesn't have an FPU and is too slow to do perspective correction, which is why games use affine mapping or interpolation on textured surfaces. This causes the texture warping on large surfaces that are common on 3D games on the PS1.
The PS1 generally had bigger and more complex games with more content due to the then massive 640 MB CD, but the N64 still had its share of great games. Goldeneye 007, Duke Nukem Zero Hour, Crusin' USA/World and San Fransisco Rush series were some of my favorites.
It wasn't the extended graphics module as that worked in my new N64...
If you mean that black expansion pack with the red top that you plug into the front top of the unit, that's not a graphics module, it's an additional 4 MB of RDRAM.
It's required for some games to run, like Perfect Dark and Donkey Kong 64. Some games will have higher graphics modes available with it installed like Duke Nukem Zero Hour, but these modes usually come at a cost of speed, the game can slow down considerably.
A bit of trivia, DK64 doesn't actually require the expansion pak. The developers forced its requirement because there was a memory leak in the game they couldn't track down, and using the expansion pack increased the amount of time the game would run without crashing. Without the expansion pak, the game would crash within a few hours IIRC.
Also about that video death issue, were you using composite out or the RF modulator? In either case, those multi-out cables were notoriously unreliable and tended to fall apart internally. I've had to rebuild my composite multi-out cable a few times.