Selecting one of those methods does not turn anti-aliasing on. The threshold comparison is computed as follows. If this difference is greater than the threshold both pixels are super-sampled. The rgb values are in the range from 0.0 to 1.0 thus the most two pixels can differ is 3.0. If the threshold is 3.0 then no anti-aliasing is done.
Lower threshold means more anti-aliasing and less speed.
Use anti-aliasing for your final version of a picture, not the rough draft. The lower the contrast, the lower the threshold should be. Higher contrast pictures can get away with higher tolerance values. Good values seem to be around 0.2 to 0.4. The second, adaptive super-sampling method starts by tracing four rays at the corners of each pixel.