What takes precedence when fatwas conflict: the strength of the argument or the attributes of the mufti?

If you are qualified to differentiate between various opinions, then you must favor what is supported by evidence. However, if you are a common person, then your duty is to emulate (taqlid) those scholars whose knowledge and piety you trust, for Allah Almighty says: "So ask the people of the remembrance if you do not know."