There are fundamental differences in the approach between the Salafi school of thought and the Ash’ari school of thought. In fact this is an apples to oranges comparison.
The Salafi school (also known as Ahl-e-Hadith) interprets religion mainly on the basis of narrations. Most salafis adhere to the Zahiri principles, which rely on the outward (zahir) meaning of expressions in the Quran and the hadith as opposed to giving any weightage to the context.
The Ash’ari school is a philosophical school of thought. The basis of understanding religion within this school (and other schools within ilm-ul-kalam) are speculative philosophical ideas as opposed to the Quran and the sunnah.