Sometimes on-demand saves money, sometimes it doesn't.
The initial cost - the cost of the equipment plus the cost of the installation - can vary quite a bit. You have to have the capacity on your gas or electric service to add this large load. Don't forget to consider the life cycle of the equipment - storage tank water heaters don't last long.
The ongoing cost is harder to nail down. The on-demand is usually less efficient heating water, but the storage tank heater has to make up heat losses from the stored water all day and night. The more the water sits unused in the tank the more heat loss there is to make up. For example if there's just one or two people in the household and they only use hot water a short period in the morning and a few hours at night, the heater spends a lot of energy just keeping water ready around the clock. For a vacation home that's only used weekends, there's even more heat lost keeping hot water on standby.
You can look even harder at the cost of the nuisance heat. In some cases nuisance heat isn't really much of a loss - the nuisance heat the water heater makes takes a little load off the furnace - others, the nuisance heat isn't just wasted, you pay for it twice - it adds a little to the air conditioning.
If you can talk to some people that have on-demand water heaters it may be more helpful than trying to do a solid to-the-penny cost analysis.