... I asked this question ages ago when I got my first 5 fin box board and wanted to know peoples opinions, which one is better. I did some research and with many opinions out there I figured the best way is to do experiments and find out for myself.
My Airush Cypher 5'10" came with 4 fins so I started with that and rode around for a few sessions. It went fine but I felt it didn't go upwind as well I hoped for so I swapped the fins out and put it in 3 fin mode. Straight away it went better upwind and made the board feel faster with gybes a little wider which I liked. I could ride fast into gybes and it wouldn't spin out or throw me off. I liked it so much better I didn't bother doing any more experiments. 4 fins felt too skiddish back then.
I rode the board like that for 8 months and recently I snapped one of the tri fins so I put the board back to quad mode and immediately felt a difference. It felt slower and but gybes were tighter. Then I pushed upwind and it was better too,,, "what the ????" I said to myself.
I found I could push the board a little harder and therefore the gybes were quicker so the G forces you get from a nice tight turn was better and way more fun, and if you really push the tail, it just grips harder and really turns fast, snappier. I also found since I could lean harder on the tail and therefore lean the rail in harder, I went upwind better with out it feeling slippy or skatey.
Ironically with more grip now I ride faster and throw myself harder into turns but if you cut back on a wave, the tail grips and won't break out as well. Not that I am any good at it, but I found it easier in tri fin mode but in quad, the board would spin around when coming off the top of a wave rather than break out.
The top end of the board is better too and I can hold down a bigger kite with good stability at speed.
At the end of the day, you got to like it so do your own experiments, you might find your head says one thing but you end up liking another like I did.
cheers,
Robbie