For better or worse, there is no one system that is universally more energy efficient and effective than the others. The one that will turn out to be the best choice for you is the one that fits best with your specific heating needs, the climate you live in and the relative price of the fuel sources available to you.
For instance, if you live in a relatively moderate climate, a heat pump may very well be a good option for you. These systems are able to operate much more efficiently than furnaces because they extract heat from the air rather than generating it themselves. That means that in the winter, a heat pump can take heat from the outdoor air and pump it indoors to heat your home. In the summer, the heat pump can actually do the opposite, taking the excess heat from indoors and transferring it out to provide you with a yearlong temperature control solution.
Heat pumps generally run on electricity which can be expensive, but since they use so much less energy than something like an electric furnace, they can still be a very energy efficient home heating option. However, these systems are not as effective in areas with harsh, long winters, and so would likely require a supplemental heating system as well. Also, the lower the outside temperature, the less efficient a heat pump is going to be.
Furnaces, on the other hand, are quite effective at heating homes no matter how harsh or cold the climate. Gas furnaces are generally the most popular of the models available now, mostly because the cost of natural gas is lower in most areas compared to the cost of other potential fuels.
However, it may be worth considering an oil or electric furnace if these types of energy sources are relatively inexpensive in your area. No matter what type of furnace you get, you’ll be able to choose how energy efficient you want it to be as well, with lower efficiency 80% AFUE furnaces costing substantially less than those with an AFUE of 90% or more.