Well it's actually really easy to do a cost comparison...
How much do you pay per therm of natural gas?
How much do you pay per KWH of electricity?
How long do you expect to live in this residence?
Here are two water heaters, one of which I actually own.
http://www.sears.com/ge-geospring-50...irectType=SRDT
http://www.energystar.gov/productfinder/product/certified-water-heaters/details/2184476
First one is the GE GEO Spring Heatpump (ELECTRIC) water heater, only $1000 maybe less if you have coupons and shit, it's pretty cheap for what it is. According to its energy guide, it will use 1830KWH in its default mode which is in hybrid mode. Hybrid mode assumes that in order to improve recovery time, like when you take a shower, it will use the resistive coils inside of the water heater to provide good recovery time AND it will run the heatpump at the same time in order to heat the water. I own this water heater.
I just did some reading and apparently, since that Geospring was released, companies are selling significantly more Heatpump water heaters of a better design by both being quieter and more efficient. Here is a Whirlpool heatpump water heater that is even more efficient and is the same price as that older design Geospring.
http://www.lowes.com/pd_89263-135-HPSE2K50HD045V_0__
Energy guide says it uses:1597KWH
http://www.energystar.gov/productfinder/product/certified-water-heaters/details/2194355
So the older GE Geospring has an Energy Factor of 2.4 while the Whirlpool and a bunch of others that have recently come onto the market have an Energy factor of 2.75. Things have advanced pretty quickly as the GE Geospring was one of the most efficient models on the market but by looking at the electric fan design (cheap fan blade design, non ECM) it was easy to see where they could make improvements to its energy efficiency.
Here is a natural gas high efficiency water heater. This one is so efficient, you'll actually have to wire up an electric fan to vent out the exhaust gasses.
http://www.homedepot.com/p/Rheem-Ec...ater-Heater-ECORHE50/203856743#specifications
According to its energy guide, it will use 183 therms per year.
One thing you should know is that these energy ratings are when the water heater is tested at 135F. Knowing a bit about the law of thermodynamics and the carnot cycle, the heatpump water heater will get significantly more efficient as you turn the temperature down. The heatpump water heater also has the benefit of selectively reducing the first hour rating by switching into heatpump only mode, making it significantly more efficient than its ratings will indicate... However on the other hand, the heatpump water heater will likely lose to the natural gas water heater if the ambient room temperature gets significantly below 45f as it will then be forced into turning on its resistive heater, making it no better than a typical electric water heater.
So in short: very cold room: Natural gas water heater wins. HOT room: Heat pump water heater wins in almost all scenarios. 60F average room temperature, then it depends on utility rates and how often you use the hot water. I will say that a heatpump water heater sounds about as loud as a room air conditioner so that may be an issue.