I largely see the benefit of a tankless hot water heater as energy savings. There is some debate as to how much longer they actually last. They have a higher combustion effeciency and you don't have to have 30-50 gallons of water constantly heated on standby.
In consideration of a rental, I would not pay between $1,500 to $2,000 for tankless instead of $500-600 tank per unit for replacement. All you will be doing is lowering your tenants gas bill and saving some energy.
Unless you are a hard core believer in Global Warming (an obivous hoax, no scientific consensus) like SOME people in Tennessee do, I would just put in the standard tank kind.
In your own home, you would need to do a cost benefit analysis of the savings in energy bill and replacement cost over the longer lasting and efficeint tank model. This depends substantially on the cost of natural gas in your area.
The tankless water heater is used much more frequently in Socialist places like Europe than America. So be careful there.
One last thing to consider is the new Socialist regime is giving out a lot of money as an incentive to make energy efficent home improvements. It may be worth it if you can get some fake money the Fed prints out of thin air to offset the cost.
Oh one last thing, from a practical standpoint, you have to let the water run for a few seconds before the water will be hot due to the distance from the heater to the faucet. This can influence the location of the installation.