This one is usually decided before a concrete crew gets a call
Slab or crawl space is a design decision, and by the time we are on the phone about it, it is normally already made. The plans say which one. Your builder priced the house around it. If an engineer is involved, the footing has been sized for it. We pour both, we have no preference we are trying to sell you, and the honest answer is that this is not our call to make.
What we can tell you is what each one means for the concrete part of the job. How many pours, in what order, what has to be settled before each one, and what it costs to change your mind after concrete is in the ground. That is worth knowing while the drawings are still on the table and changing them is free.
The ground narrows it before anyone's preference does
The lot does most of the arguing. A pad close to level takes a slab on grade cleanly, because the footing or thickened perimeter runs around at one elevation and the floor sits on compacted stone right on the ground. It is the shortest path there is from dirt to a finished floor.
Ground that runs downhill is where it gets expensive. A floor has to come out level even when the ground under it does not, and there are two ways to buy that. You haul in fill to raise the low end, which the footing then has to get down through to find bearing, or you stand a wall of increasing height on a footing that steps down the slope. The wall version is the crawl space, and on a hillside lot that is often why the drawings show one, not because anybody prefers the floor over a void. Clay sitting on rock is common here too, and the rock is often closer to the surface than the plan assumed, which is worth knowing before either build starts.
On a slab house, the concrete is largely one event
The footing or the thickened perimeter goes in, the inside gets brought up with compacted stone, the vapor barrier goes down, the steel gets set, and the slab is poured. On a monolithic design the perimeter and the floor happen together on one truck day. From your side it looks like one busy morning and then a finished floor.
Everything that has to live under that floor gets settled first, and it is a longer list than people expect. Plumbing rough in coming up through the slab. Sleeves for whatever else has to cross the slab. Blockouts. Anchor bolts pressed into the soft edge on your framer's layout. Once the concrete is finished, adding any of that means cutting the floor. That is not a disaster and it gets done, but it is a completely different job from doing it while the ground is still open.
On a crawl space house, it is two pours and a wait
The footing goes down first, steel tied into it, and something left standing in the top, dowels or a keyway, for the wall to lock into. The stem wall stands on that footing, formed in both faces with ties running through, poured, stripped and patched, and it steps down the grade in as many steps as your lot needs. There is no floor slab in the plan, since the floor system gets framed over the top of the wall instead.
The wall pour is the one that almost always wants the pump. A wall form closes up into a slot a few inches wide at the very top, and the wall itself is normally down in the hole with the dug dirt heaped alongside it. A ready mix truck loaded to capacity does not belong near the lip of an open excavation. We run a trailer mounted line pump on 2.5 inch and 3 inch line with our own operator and hose hand, so the truck can stay out on ground that will hold it while hose walks the top of the forms.
After the wall is stripped there is a window where the outside face is still reachable for coating and drainage, and then the dirt goes back. On most jobs that window belongs to your builder or your excavator rather than to us, so the only thing we ask for is a straight answer about who has it and what day.