If you're comparing Concrete Dumpster Rental to a standard dumpster rental, start here. It is dense single-material loads that need a low-side box with a marked fill line. Ask about this specifically, because it rarely comes up unless you raise it: the load only earns the recycling rate while it stays one material. Contamination costs the whole saving.
Picture the container two ways: full to the rim, or full to the ton limit. Dense debris hits the second ceiling long before it reaches the first. Contractors and landscapers typically place this order, and because the debris type is already known before pickup, the container settles into the 10 yard range without much back-and-forth. Two facts move this along: the rental window you need, and any item in the pile that requires separate handling.
Here, the truck's axle limit shows up before the container's rim does. A load of concrete or dirt can max out a container that still looks half empty. Check whether the quoted price covers one drop-off and one pickup, or whether extra trips for a swap get billed as separate visits. Don't split the difference between two sizes. Pick the one that covers the heavier estimate, because running short means a second delivery, not a partial refill.