Find out what type of system a furnace uses to produce heat. Both Lennox and Carrier produce models that operate on either gas or oil. Trane, on the other hand, produces models that run off your home's electricity in addition to the regular gas and oil models. Which one you purchase depends heavily on your home's capabilities.
Look at a furnace's "Energy Efficiency" rating. Furnaces from all three providers will have an energy efficiency rating printed in their technical specifications in the form of a percent. If a furnace has an energy efficiency rating of 95 percent, for example, this means that 95 percent of the gas, oil or electricity (depending on the model) pumped into the furnace is converted to heat for the purposes of heating your home. The higher the rating, the more energy-efficient the furnace.
Find out what type of additional temperature regulation controls are included on your furnace. For example, certain premium furnaces from Carrier also have humidity regulation controls built into the unit, allowing you to control the humidity in your home in addition to the overall temperature. Not every furnace from Lennox, Trane or Carrier has such additional controls.