From an extreme perspective:
1. Qualitative analysis method: "Buy the right company, do not consider the price."
2. Quantitative analysis method: "Buy when the price is right and do not consider the qualitative factors of the company."
Of course, in reality, both factors are considered when valuing and buying a stock or company.
A great company can be a bad investment if you overpay to own it.
Also, a lousy company can be a value trap though you paid a very low price to own it.
My personal approach.
1. The company has to always satisfy the qualitative criteria first, namely, the right company of the highest quality.
2. Having passed the qualitative hurdle, then it has also to satisfy the quantitative criteria, namely, the right price.
That is Quality first, then Price!