A common assumption is that a new, more efficient air conditioner will automatically produce a lower bill. That's true only for the portion of the system inside the cabinet. The ductwork that carries air from the equipment to the rooms is untouched by an equipment swap unless it is specifically inspected, tested, or sealed as part of the job.
If the ducts were leaking 20 or 30 percent of the air before the new unit went in, they are very likely leaking a similar share afterward. The new equipment may even run more efficiently per hour, but if a meaningful portion of what it produces never reaches a register, the house still needs more total runtime to feel comfortable — which erodes the expected savings.
A duct leakage test performed after installation tells you plainly whether the ducts are working with the new equipment or against it.