We have gotten quotes on Trane and Carrier systems. We are going to use a heat pump and gas furnace. Is Trane or Carrier the better brand?

It really all comes down to install. Both units will work just fine, but make sure you are comfortable with the installer. Any unit can break down, so make sure the installer you choose has a history of standing behind their product. There will be folks that will tell you one brand is better than the other, but if installed correctly, they are really created equal. Hvac1000 can give you info on picking a qualified installer, then go with the one you feel most comfortable with. A company that stands behind their work and product day and night is always a good indication that you will not go without heat for long if a problem does arise.