Partnarship LLC: Is it better to file article of disolution or let it go through Administrative dissolution? Is there any difference?

You are asking a legal question (which we cannot answer here), not an income tax one.

In that case, excluding the part of which is the better of the two, from an income tax perspective, is there a difference for a partnership that file article of dissolution vs. having it be Administratively dissolved?

Not really. In either case you need to wind up the affairs of the LLC and file a final return (1065), assuming you have either income or expenses that are treated as deductions or credits.