Woofer dust caps. concave or convex, what did we decide?

Yep, it’s about looks as far a I have seen. A one piece concave cone is a little more rigid in theory. Many dust caps are very porous to allow hot or compressed air to vent. Those are largely acoustically transparent. Then there is the less obvious advantage of a concave dust cap, it’s already pushed in so little kids can’t ruin your speaker by poking it in! Well, not just little kids!
Concave DCs are easier to implement on horn loaded applications with a phase plug. The other benefit is having the DC rest on the VC former top edge, for additional support and rigidity.

Convex can benefit off axis HF dispersion on a wide band or full range driver once the cone decouples from the VC radiating area, sort of what some Jordan drivers do.

A concave DC eliminates the sharp corner joining to the.cone, which can radiate off axis peaks from resonances in the cone. It also reduces the cavity volume in front of the center pole piece and raises the resonance of that.air cavity out of crossover band, which can be a big benefit.
About the only time it would make a big difference is in large diameter coils with a structural grade cap glued at the triple point. If you inverted it it would ruin the closest to equiangular "Y" formed there and throw away the available rigidity in one axis. I'm sure manufacturers of high quality high power drivers know this as I don't recall seeing a dust cap applied the "wrong" way on a real woofer, never mind inverted dome woven fiber subs and stuff like that where they employ all kinds of other heavy reinforcement there if you look at the backside of the cone.
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I had occasion to dismantle one of those Sony speakers that fascinate me, the ones with a woofer and sub-woofer in the same cabinet. The drivers are actually identical. The dust cap is used make the sub driver appear to have a bigger voice-coil and generally look 'meaner'.