What you need to look at is to look at the SEER ratings of the existing unit and that of the new unit. In 2002, you could have been sold a SEER 10. Current models start somewhere around 13 and go up from there. For very rough approximation you could use the ratio of the two, in this case 13/10 = 1.3 as the increase in efficiency, (decrease in energy cost) that you would see. So this would give you about a 30% decrease in energy cost. Use that to determine what the payback time is.

Now that is only very approximate and doesn't include possible savings from being able to operate more efficiently at lower temperatures, but it's a good go- no go method.

The air temperature coming out of the unit is not the important thing, the energy used is. Also make sure your fan is operating at the correct speed. If too high, it would show lower temps. And if this is your first heat pump, it may simply be you're not used to a heat pump. They never put out really warm air like a furnace does. (unless the back up heat comes on)

"Warmer heat" sounds like marketing hype. But more capacity or more efficiency may be reasonable ideas.

Do a search for Carrier "comfortheat" technology, this is what they may be talking about.  Typically this is achieved be the intelligent speed control of the indoor unit to provide higher discharge air temperatures than a standard heat pump.

That's the "problem" with heat pumps, they blow relatively cold air. Any heat pump blows relatively cold air, just as LarryT mentioned. For example, a gas furnace burns natural gas and blows the heated air out into your house at about 120 degrees F, where as a similarly sized heat pump will blow the air out at only 90 degrees F. Either one will efficiently keep you house at 72 degrees, they are just different in the way they do it. The "comfort heat" unit will help at startup by not kicking in the fan at high gear and blast you with the 70 degree air in your ducts and then never spinning at full speed, but even then it isn't going to give you the really hot air out your ducts that a combustion furnace will.