I have a witch farm. I have noticed, that it rarely spawns witches if my render distance is 4. But, if I set my render distance higher (say to 15) it spawns them at a fairly steady rate. [at the expense of my frame rate, and my play getting very laggy]
I also have a spider spawner XP farm, and I have noticed that the max number of spiders that ever await me when render distance is 4, is on the order of 20, but if I set the render distance higher, it's significantly higher.
Based on the above, I have two (highly related) questions:
1) According to the spawn page on the WIKI, mob spawn caps are influenced by the number of chunks "available for spawning". Is this the "Options -> Video Settings -> Render Distance" setting squared? (or there abouts)? (If so, this would explain the witch farm performance.)
2) Does the mob cap apply to mobs spawned from spawners? (If so, that would explain my spider XP farm issue. I didn't think that was always the case however.)