The distinction between qualitative and quantitative approaches is similar to the difference between human and artificial intelligence. Quantitative analysis uses exact inputs such as profit margins, debt ratios, earnings multiples, and the like. These can be plugged into a computerized model to yield an exact result, such as the fair value of a stock or a forecast for earnings growth. Of course, for the time being, a human has to write the program that crunches these numbers, and that involves a fair degree of subjective judgment. Once they are programmed, though, computers can perform quantitative analysis in fractions of a second, while it might take even the most gifted and highly-trained humans minutes or hours.
Qualitative analysis, on the other hand, deals with intangible, inexact concerns that belong to the social and experiential realm rather than the mathematical one. This approach depends on the kind of intelligence that machines (currently) lack, since things like positive associations with a brand, management trustworthiness, customer satisfaction, competitive advantage, and cultural shifts are difficult, arguably impossible, to capture with numerical inputs.