If the fins are plywood then you would be safe attaching them using either configuration.
If the fins are balsa (and the grain direction becomes important) then you should attach them the usual way.
As far as what is better, the Barrowman equations really only address fin area. They don't even consider whether the fin is nicely airfoiled or flat-plate shaped. There are a whole bunch of things that should probably be included in a stability analysis, but most of our tools don't get down to such detailed levels.
Since a fin functions as a wing on our model rockets (explanation below), it would be good to review how wings work. Classic aero theory says that wings with a short chord (distance from leading edge/LE to trailing edge/TE) and a long span are more efficient, so a fin with that shape could deliver the same aerodynamic corrective force while being smaller, lighter, and less draggy. But they are also more prone to breaking under load, and to aero flutter (if your rocket moves fast enough). You have to strike your own compromise between good performance and reasonable durability. And if you are going for a certain style or "look" then classic aero theory just doesn't matter anyway.
If you want to go for high aspect ratio fins, you can improve your odds of success a bit by using different (stronger) fin materials than balsa (like basswood, plywood, fiberglass, or even graphite composite) or by using stronger root attachments (thru-the-wall, fillets, etc).
Back to explaining fins-as-wings: When your rocket moves straight ahead, and if the fins are well aligned with the rocket's long axis, then the fins will be at zero angle of attack to the oncoming airflow. If something disturbs the orientation of the rocket from a desired flight path, and the nose tilts one way and the tail tilts the other, you don't want it to fly sideways, you generally want it to point straight ahead for maximum speed/altitude/etc. So, the fins that are also now tilted are effectively at a small angle of attack to the oncoming flow, and generate a lifting force (perpendicular to the geometric plane that the fin is in, and also perpendicular to the rear end of the rocket) that tries to push the rear end back into a streamwise orientation. When the fins generate this lifting force they act exactly like little wings and all the rules and principles of subsonic aero come into play.
You want a round, smooth LE. A square LE will generally immediately trip the airflow from laminar to turbulent, which adds drag and reduces the effectiveness of the fin. You also want a TE that more-or-less tapers down to a thin edge (it doesn't have to be a paper-thin "knife" edge) to help satisfy the Runge-Kutta assumptions on airflow around wings. You can leave a substantial portion of the chord completely flat, and just shape the LE and TE, and you will get significantly better aero performance from the fins. For competition, this might be important, and could be the difference that gets you the winning advantage in an altitude model, for instance. For sport flying, all this fin airfoiling and planform optimization really doesn't make as much difference. Personally, I believe that most kits have fins that are enough oversized that you can safely leave them square-edged, and let your rocket fly with a bunch of planks. If you don't want to mess with it, don't; if you like to mess with it, go right ahead. Fin shape will probably not make a significant difference unless your design is on the hairy edge of being unstable...but you shouldn't be designing that way anyway...
(And that was probably way more answer than you wanted)