Which is the soundest of the juristic schools of thought to follow in matters where it is difficult to determine the preponderant opinion, and what is the meaning of Ibn Taymiyyah's saying: "Ahmad's madhhab is soundest in its principles, and Malik's madhhab is soundest in its branches"?

We have already answered this in Fatwas No. 52388 and No. 92645. Preferring one jurisprudential school over another is a relative matter, so there is no problem if a scholar prefers something that another does not. Each of the four schools of thought has been chosen and preferred by a group of scholars. For the last point, we recommend reading Ibn Taymiyyah's treatise: "Raising the Blame from the Esteemed Imams."