The output of resistive devices like a heating element, varies in proportion to the square of the voltage. So the 4KW element would produce (120/240 x 120/240) x 4,000 = 1/2 x 1/2 x 4,000 = 1/4 x 4,000 = 1,000 watts. It's as simple as this.
The 1,000 watt (rating at 120V) element at 120 volts draws 1,000/120 = 8.3 amps. The 4,000 watt element at 240 volts draws 16.7 amps (4000/240). Since the 4KW rated element draws 16.7 amps at it's rated voltage of 240V versus 8.3 amps, it has to be made of heavier gauge wire. If it's about the same price, can't hurt to try it.
*Maybe* if an element is rated to operate at a higher temperature, as in operation at 4,000 watts, the exterior sheath is heavier to withstand higher temperature. In that case, I could see some merit to the idea that it would last longer at 120 volts.
But it's not normally the internal wire that burns out first (assuming normal voltage & no surges), the exterior metal sheath fails first then water gets inside and then the total failure occurs. I doubt just having a heavier gauge internal conductor (the wire that the does the heating) increases the life much, if at all. I couldn't find anything on the internet to support that idea. It's usually minerals in hard water that is hard on an element and if the sheath is the same, it won't last longer. If they made stainless steel versions of the element, that would be a good choice, but I don't know if they do for RVs.
The forum is a little screwy at the moment because of the server changes and I can't post any links. Google "Rheem + heater element failures" for some info.
You should periodically inspect inside the heater to see if there is "crud" that needs to be cleaned out. If it builds up too much, that can be hard on an element. Also make sure the anode rod is good at all times.
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