GL_EXT_shadow_funcs
The GL_EXT_shadow_funcs extension requires GL_ARB_shadow and GL_ARB_depth_texture in order to have any effect. In the GL_ARB_shadow example on this site we use GL_LEQUAL when setting the GL_TEXTURE_COMPARE_FUNC_ARB texture parameter. GL_ARB_shadow allows this comparison function to be GL_GEQUAL as well, but not any of the other comparison functions.
This extension allows us to use GL_GREATER or GL_EQUAL or any of the eight comparison functions given to us by OpenGL. However, these other functions will not show you much difference. GL_LEQUAL and GL_LESS will look very similar, GL_EQUAL will most likely not be worth using, nor would any of the other comparison functions that this extension gives you. The reasons why you won’t see any difference are given in the extension specifications:
Are there issues with GL_EQUAL and GL_NOTEQUAL?
The GL_EQUAL mode (and GL_NOTEQUAL) may be difficult to obtain well-defined behavior from. This is because there is no guarantee that the divide done by the shadow mapping r/q division is going to exactly match the z/w perspective divide and depth range scale & bias used to generate depth values. Perhaps it can work in a well-defined manner in orthographic views or if you can guarantee that the texture hardware’s r/q is computed with the same hardware used to compute z/w (NVIDIA’s NV_texture_shader extension can provide such a guarantee).
Similiarly, GL_LESS and GL_GREATER are only different from GL_LEQUAL and GL_GEQUAL respectively by a single unit of depth precision which may make the difference between these modes very subtle.
So, unless you are using very specific hardware, you will most likely never need these extra functions.