OK, you have a piece of wire submerged under water, and you pass 1 volt at 1 amp through it. Ohms law will tell you that you're passing 1W of energy through this piece of wire. What does it do? Gets hot. ALL of the energy you're putting into this wire (or heating element, if you'd prefer) is being turned into heat, and is heating the water. You have 1W of electrical energy going in, and 1W of heat is going into the water as a result. It's 100% efficient.
What happens if you apply power to an electric motor? It spins, as you would expect, but it also gets warm. This warmth is energy that has been LOST inside the motor and is being released as heat. A quick Googling would reveal about the absolute highest efficiency motor we've achieved is about 92%, and typically above about 70%. This caps any device using a motor INSTANTLY to a max of 92% efficiency, and we aren't even talking about heating water yet. You've already wasted 8% of your input power (assuming you're using the most efficient motor currently available) just running the motor. Just THIS fact ALONE means this device can not be more efficient than a heating element.
Seeing as we're on the topic of efficiently heating water, there IS a way to "heat" (quotes are important here) water using less input power than a heating element, but it's generally not referred to as "efficiency". This is using heat pumps, and as you would expect, they do it by moving heat from one source to another. In the case of heat pump water heaters, they move heat from the surrounding air into the water. They are able to move more energy into the water than they actually draw in electrical power, thus the confusion as to how they can be over 100% "efficient". They're not turning the electrical power into heat (though a good portion of it is wasted as such in the compressor motor), but instead just moving it. Therefore, in order for it to be able to heat the water, it must already have an existing supply of energy in the form of heat. Even freezing cold air is still a couple hundred degrees above absolute zero, however the larger the differential, the less efficient (at moving heat, not how much power they draw) they become.