Interim differences summarised:
Cloth seat is more comfortable than a rigid seat even with padding. Pressure points (your sit bones) will compress padding to a rigid seat, where a cloth seat would be more forgiving.
Cloth seat has better ventilation, assuming an open fabric is used. This allows airflow through and sweat to come out.
Rigid seat provides more elbow room, where the rails of a cloth seat could interfere.
Rigid seat is more aerodynamic because it is completely behind the rider's torso.
Cloth seat is slightly safer because it does poke out further than the rider. This would protect the rider from the ground if sliding, or slightly from intruding objects.
Cloth seat frame could be built taller to form a roll-bar to add supports for a roof/rain deflector/sunshade
Cloth seat is safer because your bum and back are slightly cupped, where a rigid seat is less cuppy so you could slide sideways easier. Probably more of an issue on a trike where there is no leaning into corners.
Cloth seat frame might be engineered to fold, making the seat pan adjustable separately to the seat back. A rigid seat would only be able to tilt on its mount points.
Rigid seat presents more power because the rider's back is firmly supported, where a cloth seat has more give and will flex on every power stroke.
Cloth seat is easier to build (this is debatable)
Both seat styles support a headrest of some sort.
Both can be under a kilogram total, or as heavy as you want.
Both can have their cloth/padding parts removable for washing.
I'll come back with more information in a couple months.