... my reply is not going to be very technical but my experiences might help.
Quad vs Tri made a huge difference for me on my board (Airush Cypher 5'10"). I learned on a directional a million years ago and quickly went to TT in the beginning so going back to directional boards was like learning again, especially strapless. Having 5 fin boxes, I didn't know which way I would like it so I did some experiments. And to muddy the waters, my board's fin boxes have the ability to adjust the position fore/aft by a couple of cm too.
Experiment one was since the board came with 4 fins as standard, I put all of them in and all the way back then got used to the board.
My next experiment was to take rear pair of fins out and try the tri configuration and I instantly liked it. The board tracked better and I felt I could go upwind a little better. Some how, less fin area gave me more drive upwind and it didn't feel so twitchy.
Next I pushed all 3 fins forward in the boxes and it loosened up, still a smooth feel and way more manourverable but without the twitchy feel I felt in 4 fin mode. I get to snap gybes quicker than when fins were back but not throw me off like the 4 fins did. I think since the rear fin can be 'broken' out easier than 2 rear fins, its alot more forgiving and makes the board reward little mistakes instead of kicking you off.
So, from what I found, if your more experienced and aggressive and want more snap, 4 fins is the go, but if your in the mood for more carve, drawn out gybes, tri fin is the go.
Hope this helps?
cheers for now,
Robbie