I have two LEDs with the same energy irradiance, 10 mW/sr for a solid-angle of 0.01 sr, but with different emission half-angles: LED A = 15° and LED B = 45°. Can I say that they will emit the same energy for the same solid-angle, independent of the half-angle?
So what these measurements are saying is that the irradiance is 10 mW/sr when measured over 0.01 sr. Since the half angles are different this unity of measurement only applies to the peak value (presumably the center). The reason is that the half angles are different and presumably the irradiance at that half angle is the same.
Put another way, at 7.5 degrees (don't you love the mixing up of units ?) you are half way to the half angle LED A but one sixth of the way to the half angle for LED B.