How can you ever call anything with a heat pump efficient? Especially when compared to your back up of gas.
I've just researched and installed a system in my house and nothing beat my high efficiency gas heat except for geothermal which simply cost too much down here to even be a contender......
http://tinyurl.com/3dm4mm
Geothermal IS a heat pump!!! It's just a different type. a "ground-source" heat pump, as opposed to "air-source" which is the more common type, which does need a backup in extremely cold temperatures.
The reason "the most efficient" type of heat is never really discussed, is it's not a black & white answer. There are too many variables. Kind of like asking "what is the best car" or "where is the best place to live" There are plusses and minuses of each.
For "most efficient" I'll assume you mean heat output, per dollar spent on energy, ignoring installation costs. If you factor in installation cost, you throw a completely new variable into the mix.
For the specific question of energy out, per dollar spent on energy, the answer would be any type of heat where you don't have to pay for the energy in. I.e. solar, wind, micro-hydroelectric, etc... anything where you can take something you can get for free, and extract usable energy from it. The problem with all of those is extremely high installation cost, especially when you need to store energy for the nightime and/or no-wind periods. If you're looking at pure operating cost only, not installation cost, those will always win. (of course, eventually, you will have some kind of maintenence cost associated with all of those, but i'll ignore that for now, since that's long-term future cost, and hard to estimate)
Next would be sources that you have to use a small amount of energy to "extract" a fuel that you can get for free. For example, wood, if you have lots of trees available to you. You still need to cut and split the wood. That does take some energy (however small), whether it's fuel for tools, or extra food you have to eat, so you can use your muscles to cut and split. In this example, the energy expended is a very, very small portion of the energy in the wood that you're "extracting" or "unlocking" by turning standing trees, into a usable product. However, you still need to pay property taxes on the land you need to own, so you can have the trees for "free", so there those trees really aren't "free" are they? i'll ignore that one for now. Here you're looking at "extracting" hundreds or thousands of times as much energy as you used to extract it. In this category would also be heat pumps (without "backup" heat). You use a comparatively smaller amount of electricity to "extract" free heat from the ground or the air. Of course, heat pumps only "extract" 2-4 times the amount of energy (electrical) that you need to put in. Because of this, and the fact that "air-source" type works very poorly at low ambient temperatures, they may, or may not be cheaper to operate than some items in the next category, depending on electricity cost and competing fuel costs
Next up would be all of the systems using conventional fuels. Electric (resistance heat), gas, oil, pellet, corn, etc... for those, they all depend on particular costs of those fuels in your area, and the unit efficiency.
Now, for example, if you were looking for highest efficiency (not lowest energy cost), energy in to usable energy out, electric resistance would be the "best" 100% of the energy in becomes heat. Of course, the cost per BTU of electricity is much higher, so even though this is the highest efficiency, it's not the lowest cost.
Heat pump (either ground-source, or air-source) is not really applicable here. I know someone will say " my geothermal heat pump is 350% efficient". Well, not really. You get out 2-4x the amount of ELECTRICITY you put in, but not 2-4X the ENERGY you put in. Remember, the heat pump is taking electrical energy AND energy out of the ground, or the air. One energy you have to pay for, and one you don't. Energy can not be created or destroyed, so nothing can be over 100% efficient, when you look at ALL the energy put into the system, not just the one that you pay for. In fact, many systems are 100% efficient at making heat, they're just not all that efficient at making USABLE heat.
Hope that wasn't too confusing (BTW... yes, i'm an engineer with an interest in energy conversion, as we call it.)
Hybrid heat . Heat Pump with gas or LP backup heat instead of electric backup if its over 35 * outside the heat pump provides your heat under 35* the fossil fuel furnace provides the heat PLUUUUUS you'll have AC in the summer 
