There hasn't been an direct on-screen conflict between two Shard holders yet; the closest we came was the conflict between Preservation and Ruin, as you pointed out, and that's not really the same thing. (In that case, the two shards happened to be in direct opposition to each other's nature, so it was natural that they'd conflict.)
However, we find out in the Stormlight Archives novels that Rayse (Odium) has been world-hopping to the various Shard worlds and killing off their Shard holders. The chapter intros from Part 2 of The Way of Kings make up a letter between two people who are clearly Cosmere-aware. Whoever is writing the letter (we assume it was Hoid) explicitly claims that Odium murdered Skai (Dominion) and Aona (Devotion) on Sel, the world of Elantris, and splintered their Shards. We also know from Dalinar's visions that Rayse is the one who murdered Tanavast (Honor) on Roshar, the world of the Stormlight Archives.
The chapter headers from Part 4 of Words of Radience form a response letter, from a currently-unknown person, which claims that Tanavast's sacrifice has somehow trapped Rayse on Roshar. It's basically implied that this is the only reason he hasn't killed anyone else since Tanavast.
While the death's of Skai and Aona sound more like assassinations, the fight between Rayse and Tanavast was clearly a war -- the war that makes up the history of Roshar, which we see bits and pieces of in The Way of Kings opening scene and Danlinar's various flashback visions. (A war that Tanavast, obviously, lost.)