Do you have natural gas installed at your house? If so, it probably makes sense to switch to a natural gas water heater. With current energy use and pricing, those are always cheaper to operate than electric heaters.
After that, it's important to consider how you use water. Long showers, or short? 1 person in the house, or 7 (Whoa, that would be a lot). If you use a lot of hot water, the tankless natural gas heaters may be a good idea. Depending on what model you get, they can be quite a reasonable price. A smaller unit, capable of delivering hot water to "only" 2-3 showers at a time through Rinnai, can be bought for something like $300-400. And they are more efficient, so using more water means more savings. Another thought, somebody else mentioned the cold water sandwhich problem. I have two comments on that:
1. This can be mitigated by the design of your plumbing system. If the shower is really close to the water heater, and there's very little plumbing in between, you're gonna have a problem. But it your shower is in the far corner of a large house, then there's enough heat in the water/pipes between the water heater and the shower that people rarely encounter that problem.
2. It can be mitigated by including a small buffer tank in the water heater. The Navien tankless water heater does this, and recirculates water through a 0.5 gal tank to keep that buffer hot at all times. They avoid the cold water sandwhich problem that way. I personally think it's a pretty silly solution, that obviously decreases the efficiency of your high efficiency equipment, but it does mitigate the cold water sandwhich while still being more efficient than storage tank water heaters.
If you don't have natural gas on site, the highly efficient option is a heat pump water heater. They're efficient, and expensive. The choice again comes back to how much hot water you use, and what you care about. If you use a lot of water, it may be an economical choice. If you care a lot about energy efficiency, even if it isn't economical, it's a good choice. If you use a little water, and are primarily motivated by the economics, it isn't. In that case, it's probably best to stick with the electric resistance tank and look at other ways to save on water heating energy use (Low flow fixtures for example).