Propane is generally less expensive for heating water than electricity. In addition, propane heats water roughly twice as fast as electricity.

Below is an energy calculator. Before you log on, you will need to know what you pay fo relectricity (per kWh) and Propane (per gallon).

Here is a link that might be useful: Energy calculator

If you were to experience a extended power outage the LP water heater will continue to produce all the hot water you need.

Thanks to both who have answered so far! More please....
Yes, you are both right on each of the thoughts, BUT.... our propane is quite expensive ($2.50/ gal) and has been on a huge rise for years. We are a level pay plan that locks the cost in once a year and we pay a set amount each month based on usage and projected usage.
The electricity, on the other hand is a yearly average of 6.36 cents/kwh. Any calculator that I have found that compares just average amounts used has the propane much cheaper than ours and the electricity much higher. That is the reason for the dilemma. Our costs are outrageous because of the inefficient old water heter AND because of the propane costs, so much so that it seems that I could pay for the new one with installation and adding a new electric line for the less than the cost of gas for a year! Hence the question- it seems like a no brainer, but I need a devil's advocate here.
The thought of not having hot water during electirc outagages was thought of but since with no electricity, one could not dry one's hair in a cold house, one might not be bathing. Keep the thoughts coming, please!

Try this calculator.

For $0.0636 electric and $2.50 LP, even assuming 90% efficiency for lp (unlikely) and only 94% for electric (which is quite doable - look at a Marathon water heater), lp is almost twice as expensive. For "normal" efficiencies, it is twice as expensive.

Here is a link that might be useful: Multiple source energy cost calculator

The magic number you're looking for is 27. Efficiencies aren't *that* different, so the main thing you're looking at is how much you pay for a unit of heat energy. A gallon of liquid propane contains the equivalent of 27 KWH, so your 6.36 per KWH electricity translates to $1.72 per gallon propane and electricity is about 30% cheaper, maybe a little more when you factor in efficiency. There are several thing you should consider. One requires predicting the future prices of both electricity and propane. Electric rates have been known to change suddenly in some parts of the country. Propane is mostly refined from oil; oil may be a near term peak or we may be running out as some say and will only get pricier. Another thing that may not be a factor with your large tank: recovery time, in other words, how fast can you make more hot water when you use it. Gas water heaters are generally superior in this respect, making more hot water at up to twice the rate of an equivalent electric model. Finally, as others have mentioned, how reliable is your electricity. If you get frequent long outages, that would favor propane.

Some high efficient gas water heaters also require electricity for pilotless ignition, heat recirculation fans, etc. If the electricity goes out, the gas won't light so you're no less vulnerable in an emergency. I use natural gas and I don't know if this applies to heaters using propane, but it's something to consider.

The only way to do it is to perform the full calculation, and also take into account fluctuations in the prices of both. I suspect LP is more expensive because of the delivery.

That said, it is *pointless* to consider the efficiency of your current water heater. It is as you say old and inefficient (even more so than when new). Your bills will go down either way, the question is by how much.

We have natural gas, but that's piped in. LP could go "out" like electricity if you can't get access to it for some reason (e.g., heavy snow, supply disruption, etc.), so it's not perfect in that way either.

I just used Colin's link above. My LP costs $2.60/gal and my electricity $.06/kWh, neither of which is too far off from OP, which is why I am posting this. The calculator (the second chart) says my LP setup is saving me a considerable amount.

I should add: I have a tankless water heater, which may render the calculation irrelevant, though I am not sure.