Foam is lighter, cures in about 15 minutes, is waterproof, and uses penny-sized holes, so it is our default for most residential slabs. Mudjacking uses a heavier cement slurry and bigger holes and can be cheaper for some jobs but adds weight to the soil. Foam wins for driveways, garages, and steps.
More detail
Both methods raise a settled slab by filling the voids beneath it, but the material and the holes differ. Polyurethane foam jacking injects a two-part expanding polymer through small ports about the diameter of a penny; the foam expands to fill voids and lift the slab, cures hard in roughly 15 minutes, is waterproof, and is very lightweight, around 4 pounds per cubic foot. That last point matters: because the foam adds almost no weight to the soil, it does not contribute to the very settlement you are trying to fix, which is a real advantage on the weak clay soils common around Cincinnati. The small ports are easy to patch and the slab is usable the same day. Mudjacking (also called slabjacking) pumps a slurry of cement, sand, and water through larger holes, typically 1.5 to 2 inches across, to float the slab back up. It is a proven, decades-old method and can be less expensive per job, but the slurry is heavy (roughly 100 pounds per cubic foot), the larger holes are more visible after patching, and the added weight is a drawback on soils that settled because they could not carry load. For most residential leveling, garage floors, basement slabs, driveways, sidewalks, patios, pool decks, and front steps, we default to foam because it is cleaner, lighter, faster-curing, and longer-lasting in our soil conditions. We will recommend mudjacking when it genuinely fits the job and the budget. Either way, leveling addresses the symptom; if a downspout, plumbing leak, or eroding fill is creating the voids, that source needs attention too or the slab can re-settle.