You fly both. It’s a cutter. It’s meant to use both. It’s not meant to be an either/or option package.
In rough weather the best storm set for a cutter or double-headsail ketch or yawl is the little jib on the inner forestay, by itself. It will hold the boat just off the wind, at maybe like 35-40 degrees, and it is low enough to effect enough heel to stabilize the boat while not making it heel too far.
My recommendation is always to get rid of the staysail boom which only divides the deck and makes it very hard to go forward (you’ll always be on the wrong side of it). Headsail booms are great for very large boats on which you can walk under the boom (or at least duck). On smaller boats (up to 65’?) it’s best to just have two roller-furlers and fly them both loose-footed. The small one can be like a little 110 or 115, coming a little aft of the mast and sheeted to a track inboard on the side deck or on the cabintop. The big one can be like a 135 with a high clew (for visibility) sheeted back to the cockpit possibly through (big) turning blocks. This arrangement gives you the best variety for the most conditions.
You will need two sets of sheet winches in the cockpit. And be sure your turning blocks are strong enough (2x rated load - they’re doing a 180. Schaefer 7-series should be okay for an H37).
And yes, naysayers, you CAN tack the outer jib between the two forestays. Just be sure to use sheets spliced to the clew or else a double-ended sheet with a cow hitch at the clew, to ensure no bowlines or (worse) shackles snag on the stay going around.
And here is the boat I learned all this on (note furlers) -