How to deal with the disagreement among hadith scholars regarding the authentication and weakening of hadiths?

The Shaykh : Now we enter into the core of the subject. We begin with the early hadith scholars, then we turn to the modern hadith scholars of today. If al-Bukhari authenticated a hadith and Muslim weakened it, one’s soul is reassured by al-Bukhari’s authentication rather than Muslim’s weakening. Do not forget that in our research, we do not have criteria for preference (murajihat) that say, “This one authenticated it and this one weakened it.” We say, “We accept al-Bukhari’s authentication and leave aside Muslim’s weakening.” The issue may be the opposite: a hadith that al-Bukhari weakened and Muslim authenticated. This occurs frequently. One who does not have another criterion for preference is undoubtedly reassured by al-Bukhari’s statement, whether it is authentication, weakening, vindication, or criticism. His statement is preferred over the statement of one below him in knowledge, such as Muslim, despite his fame in knowledge.
This is in addition to the case where al-Bukhari contradicts some of the later scholars, such as al-Daraqutni, for example, or Ibn Hibban, or others. This is undoubtedly one of the criteria for preference.