Water Heaters - Worth while to replace electric water heater?

I have been tossing this question around for 6 months and looking for opinions. I have lived in my house for four years, and the whole time our electric bill is very high. My neighbor who has an identical house and has about the same appliances and number of people living there, has an electric bill that is less than half of ours. The only thing left I can think of is the water heater. I don't know the brand, but it is a 40 gallon electric and my guess is at least 10 - 15 years old.... possibly older. My question is, would it be possible for this thing to be using that much electricity? Also, I know it probably doesn't have much of a life left, but are new ones really much more efficiant than say 10 years ago? Also, would there be a way to test if this is the problem? Like I said, I know they are only expected to last maybe 15 years but it works fine, just don't want to replace it if it isn't going to make that much of a difference. Anybody have any ideas?
Thanks

Touch the tank and see if the top is warm. If so, what temperature is it? Is it a a degree or two warmer or is it 5 or even 10°? Unless it's warmer, it's not wasting heat.

Maybe check your water meters and compare total daily shower times with your neighbour and see how much that explains? An old fridge or freezer perhaps?

Is your water heater on its own meter? Where I live, they usually have them on their own meters because they get a discounted rate.

Less usage of power? Does the neighbor have more insulation and better weatherstripping? Air gaps to attic sealed? Heating thermostat set lower? Changes filters frequently? Laundry not done during peak hours when many companies charge a higher rate? Newer, more energy efficient appliances? Energy efficient lighting? More energy efficient windows? Closes curtains to keep heat in?