I think this question is impossible to answer without clarifying a couple of things.
- No book of the Bible has "absolute authority in religious matters". When Christians talk about the authority of scripture they do so with an understanding that the authority of scripture is simply a shorthand way of saying "the authority of God exercised through scripture." For more on this see my post that reviews N.T. Wright's book "The Last Word" [HERE]
- The authority of the Bible is not complete if parts are removed. If one believes that "the Holy Scripture, the Old and the New Testament, is the Word of God and the only perfect rule for faith, doctrine, and conduct" (as do most protestants, including my own denomination) then you can't accept part of it without taking another part too. In this view scripture interprets scripture and so all of scripture must be in the conversation.
- The real issue here is, "where does one go to form Dogmatic formulations of "proofs" for dogmatic formulations?" This is a much more serious matter. In all honesty few Christians who argue for the "absolute" authority of scripture for dogma go to the psalms, or the wisdom literature for their central dogmatic formulations. Most tend to live almost exclusively in the writings of Paul (and we can thank Martin Luther for that). This was not always the case, Jesus himself seemed to express His own christology through the psalms more then anything else. In fact, the New Testament writers as a whole quote from Psalms more than any other Old Testament book.
"if we were going to try to "do theology" from one collection of writings or the other,This question is a little easier. I would tend to go to the Psalms MORE OFTEN.
which one would be more useful?"
Jesus went to the psalms more.
The apostles went to the Psalms more.
The Church fathers went to the psalms more.
I, too, would go to the psalms.
Wisdom literature is just that, it's wisdom. It mostly includes the kinds of things that any person who has lived can say about life. It's a good reservoir to drink from if you are seeking a better way to live, but it doesn't say much about how things change when God shows up.
Psalms, on the other hand, reflects upon how one lives with God.
Advice about how to live with God can't be done by anyone. It has to be done out of a place of encounter.
Theology literally means "a word about God." Proverbs can't achieve true theology because they express platitudes rather then rendezvous.
Proverbs points toward a collective human experience (even if it's impetuous is divine). Psalmists begin with the life of faith with a personal (eminent, tangible, relational) God.
Wisdom is common sense seeking imitation.
The Psalms are faith seeking understanding.
BOTH are valuable, but is more useful in theology