Just to confuse issues, smore ramblings...
Does the floor require a Fire Resistance Rating? if so, by the ceiling, by spray, or by assembly? I've also used OWSJ in composite manner... many tests have shown, the puddle welds attaching the deck to the joists generally cause composite action for a significant portion of the live load. As your live load increases, the cost benefits of composite design become more significant.
A typical assembly might be: Steel composite purlins at 10' o/c framing into composite girders with a 3" deck and 3-1/2"semi-lightweight conc topping. The beams and girders have firespray... The deck assembly does not... another might be OWSJ @ 2' o/c with 2-1/2" topping on V-rib form... dramatically different.
There are a pile of assemblies, with various deck thicknesses, joist/purlin spacings, and different toppings. The cost of each varies from locale to locale.
OWSJ may have problems with firespray. If you have sufficient floor area, you might want to do a prelim design of a couple of framing schemes and have them costed... The entire assembly should be costed.
If all else fails, the framing using OWSJ may be more economical, but will provide a greater depth of structure. If it's a small area, then run with what the Arch has sketched advising him that you haven't done any cost comparisons. If you have a large floor area, then the added savings warrants a bit of investigation.
Dik