The versifier said:
“A group once disputed before me about al-Bukhari and Muslim,
asking, ‘Which of the two should be given precedence?’
I replied, ‘In sheer soundness al-Bukhari is superior,
while in elegance of arrangement Muslim excels.’”

In other words, Muslim’s ordering of material and his presentation of the various lines of transmission is finer, but in terms of authenticity al-Bukhari surpasses Muslim.

When we study hadith, authenticity concerns us more than style or literary craftsmanship.

Thus the reports are ranked in seven tiers:
1 – Those on which al-Bukhari and Muslim are both agreed.
2 – Those recorded solely by al-Bukhari.
3 – Those recorded solely by Muslim.
4 – Those that meet the joint criterion of both. At times this is expressed as “according to the criterion of the two Sahihs” or “according to the criterion of al-Bukhari and Muslim.”
5 – Those that meet al-Bukhari’s criterion.
6 – Those that meet Muslim’s criterion.
7 – Those that satisfy the criterion of scholars other than the two.

Third Discussion
Is every narration on which al-Bukhari and Muslim agreed authentic—so that we need neither examine its narrators nor question its wording?

The majority of scholars maintain that everything contained in the two Sahihs is authentic and conveys knowledge, for the Muslim community has received both books with acceptance, and the community is protected from unanimous error. This is the view of Ibn al-Salah, and, I believe, of Shaykh al-Islam Ibn Taymiyyah and his student Ibn al-Qayyim (may Allah have mercy on them).