The technical differences in the quality levels are known only to madshi but they are probably something like number of neurons used, a pure speed v.s. quality trade-off. The quality levels don't really change the sharpness, they change the precision of the predictions.
The differences between Soft, Standard, Sharp, and AA are differences in the algorithms themselves, for example Sharp is very sharp at all quality levels and AA is softer and anti-aliases well at all quality levels. Normal and Soft are simply less sharp versions of the Sharp algorithm while AA behaves slightly differently. AA does not have a direct quadrupling mode and shifts the image very slightly up and to the left. Performance is similar between them all, with the exception that direct quadrupling is faster than doubling twice.
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