I don't know if diamonds spawn less in mountains and extreme hills biomes or not, but I always seem to get extreme-hilly unlucky (sorry) with finding diamonds in those biomes. The other day I spent hours strip mining a huge square shape underground underneath the extreme hills biome and mined many thousands of blocks until I finally found 1 diamond ore. Usually mining like that in any other biome for that period of time straight would get me at least 24 diamonds, enough to make a full armour set and I was using an efficiency V pick with unbreaking III and mending so I didn't ever have to stop to repair it or anything.
The minecraft wiki states that "Diamond ore attempts to generate 1 time per chunk in veins of sizes 1 to 10, from altitudes 0 to 15, in all biomes." When mining I like to mine in mountain biomes as you may come across emeralds however diamonds can be found everywhere. I begin by creating a root corridor on y axis:12 mine a 1x3 tunnel forward approximately 20 blocks out from this one then return. I then miss two blocks and mine down another 20 blocks etc. I find that once you can see a block isn't diamond there's no reason to mine it. When using this method I like to have a large stack of gates so they can be placed in each corridor to avoid getting lost as I grows.