There are a lot of "It depends" to factor in your question. Electricity rates if you are on a metered site, LP gas prices locally, and ground water temperature wherever you are located. Here's a spec sheet on a Suburban 12 gallon tank model, I would think other brands will be similar:
12 Gallon Suburban Advantage Tank Water Heater with Direct Spark Ignition
suburbanrv.com
It shows a recovery rate of 10.1 gallons/hour on gas, and 6.1 gallons/hour on electric; the gas has a 65% faster recovery rate.
RV water heaters commonly have a fixed 130 degree thermostat, you can't adjust that. This is where the ground water (incoming water supply) temperature is important. If you are in south TX, FL, or AZ you might have 75 degree water, whereas if you're in WI, MN it might be 42 degree water. Does the water heater have to raise the temperature of that 12 gallons of water by 88 degrees or by 55 degrees? Obviously this will determine the length of time the burner and/or element has to run to achieve this.
Suburban specs show a 1440 watt electric element, this is one of the largest loads on your system, about what an AC is, you just don't have the surge or inrush when it starts. If you are on a metered site, electricity rates are likely regulated by the state's Public Service Commission. In addition to the base price per KWH, they usually have a fuel adjustment price that can vary a bit plus a daily or monthly service charge. The only one I'm familiar with is my utility which is $0.53/day; in other words, if I don't even turn a single light on, I still have to pay the $0.53 for the day. The 1440 watt element will burn 1.44 kilowatts per hour.
LP gas is unregulated and prices vary from location to location and there tends to be a lot of opportunistic dealers like the campgrounds that sell it. The 12,000 BTU burner will burn about 0.15 gallons of LP per hour. There's also a convenience factor that may or may not be important to you. The electricity will always be on, whereas you'll have to remove the tank load it up and drive to a dealer for refill. LP tanks tend to go empty at the most inopportune times.
The tank will take about 2 hours to heat on electric, and about 1 hour and 10 minutes on LP. You can run both at the same time and theoretically heat the tank in about 45 minutes. I normally turn both on when I first set the rig up and turn the gas off after that. I like to have some good hot water for a hand wash after handling the hoses, cables, etc. This probably won't apply to your case but could be used if 2 people like to shower within a short time period.
Here's a rough calculation comparison; I based it on 55 degree water supply and heating the entire 12 gallons to 130 degrees, and arbitrary prices for electricity and LP:
Electricity: 1440 watts X 1.96 hours=2.8 kilowatt hours @ $0.12 per KWH= $0.34
LP gas: 12,000 BTU X 1.19 hours @ 0.15 gallons (LP) per hour = 0.18 gallons X $3.00/gallon = $0.54
You can research electricity and LP prices for your location and do your own calculations. Electricity will probably always be a little cheaper but slower. If your electricity is included in your weekly/monthly rent at the site, it's a no brainer.