Determine your hot water needs.
A tank style system holds a certain amount of hot water and heats it up to the specified temperature. Then, it is delivered to the tap. If you run two showers, a dishwasher and a clothes washer all at the same time, chances are you have a water heater that is large enough to handle this.
A tankless system heats the water at the moment you request it from the tap, there is no reserve; the water is being heated on its way to the tap. The tankless system may not be able to keep up with the high demand mentioned above.
Review tank placement.
A tankless system requires that it is vented though an outside wall. Thus, it must be mounted to a wall that is on the outside of your house.
A standard tank system can be placed just about anywhere, as long as there is a water line, and gas and/or electric line available.
Consider Installation costs.
Tankless systems require installation by a certified plumber and electrician, because of the challenges inherent in routing water, electric and/or gas.
A standard tank type system can be installed by a talented amateur, as long as you follow the directions.
Compare the efficiency
The efficiency of the tankless system does not decrease over its lifespan; it will heat the water just as well in 10 years as it does today.
A tank system will lose its efficiency as it ages, due to rust and sediment build up in the tank itself. Also the heating element becomes less effective as it gets older, due to mineral deposit buildup.
Select gas or electric.
If you are replacing your existing hot water heater, choose the same style as you currently have. That is, if you have a gas heater, choose another gas heater; the same goes for electric.
A tankless gas heater must be vented through an outside wall; a gas tank type system may not.
An electric tankless system runs on 220v electricity, if your home is not setup for 220v, you will need to have that installed.
Tips
Whichever system you choose, be sure to check with your local building codes for proper placement of the vent (if necessary), as well as any rules regarding hot water heaters.