Since conventional water heaters operate by continually heating up a full tank of water, they are much more expensive to operate, opposed to any of the tankless water heater varieties. Tankless water heaters have a much more efficient design, one that allows heating the water when one needs it, which give the benefit of continuous hot water, while saving you money. For example, running an electric tankless water heater typically yields a 10-20% reduction in costs compared to a conventional water heater. Running a gas tankless water heater can have as much as 20-40% in savings.
Besides cost savings, tankless water heaters are also more reliable long term. There is a long known issue of corrosion on conventional water heaters that lower the life span and creates a hassle in maintenance of it. This is one of the reasons why a conventional (tank) water heater can last anywhere from 5-15 years, depending on the quality of water heater, quality of water running through it, and how much you maintain it. Tankless water heaters on the other hand do not have these and other issues and easily last upwards of 20 years.