The big decision: tank Vs. tankless gas water heater

Tankless gas water heaters offer the following advantages over traditional tank-style water heaters:
-Ability to provide endless hot water on demand
-Higher energy efficiency
-Lower operating costs (see energy calculator below)
-Space savings

Note: Typically (but not always), condensing tankless gas water heaters have two heat exchangers, and non-condensing models only have one.
The extra heat exchanger in condensing tankless gas water heaters uses heat from the exhaust gas to preheat the inflowing cold water. This means condensing tankless gas water heaters are more energy efficient, and have cooler exhaust gas to vent.
Source: Navien – 

Also, Condensing tankless gas water heaters require  proper disposition of acidic condensate.

Standard Gas Water Heater
~$2,000 to $3,000 product + installation by licensed plumber 
Local Utility rebates on ENERGY STAR® certified models up to $700
Natural gas operating cost ~$300/year
Propane gas operating cost ~$500/year
Tankless Gas Water Heater
~$4,000 to $7,000 product + installation by licensed plumber 
Local Utility rebates on ENERGY STAR® certified models up to $1,500
Natural gas operating cost ~$240/year
Propane gas operating cost ~$500/year

Annual Energy Use comparison Calculator (Natural Gas)

Water Heater Annual Cost & Savings Calculator

Water Heater Energy Comparison

1/ 40-Gal Tank (UEF 0.67): $0.00
2/ Tankless Condensing (UEF 0.95): $0.00
Annual Savings Estimate: $0.00
*Estimates based on an average household load of ~210 therms baseline energy requirement adjusted for UEF efficiency, paired with state-specific average utility rates.

Resources: Basic principles to properly size a tankless gas water heater