Burton's writing credits are as follows:
KEA - Anesthesia (sole writer)
RTL - co-writer on every song except Trapped and Escape
MOP - co-writer on title track, Orion and Damage
Note that order of the writing credits varies from song to song, and I assume there's some significance to that. Burton is the first listed writer on Fight Fire, Bell, Fade, Creep, MOP and Orion.
Ulrich is often quoted as saying that Burton was the only member of the band who really understood music theory. That translated far more to writing than it did to playing, although songs like Anesthesia, Ktulu and Orion are songs where he really shines as a player.
However, as I mentioned previously, his playing generally tracked the rhythm guitar - songs like Bell (other than the intro), Fade, Creep, Battery, MOP, Heroes, Damage and pretty much everything on KEA.
That the band released the Cliff Em All video really helped his reputation. It was the first time I learned that the intro to Bell was done on bass (and a big reason why I bought a wah pedal for my bass).