7 tons is a lot of output. Is it a very large or poorly insulated house? Or perhaps one needing extra output because of a cold climate serviced by the heat pumps?

Note that the Carrier 24 requires a fancy-pants, proprietary, and expensive Infinity System Control, not a conventional thermostat. The Carrier Performance 16 uses a conventional two-stage thermostat. I recently bought a Carrier two-stage packaged heat pump and like the two-stage operation because it allows the compressor to operate more quietly, match the heating needs of my condo better, and support a slower blower speed in stage-1 which results in less air-flow noise.

Note that Carrier Corp sells the same* (but not all) products under its many brands: Carrier, Bryant, Arcoair, Heil, Tempstar, Comfortmaker, Day & Night. You can safely buy any of these and get the same product. Just check the web sites and compare spec sheets.

Trane and American Standard heat pumps are also the same*.

*They just look a little different.

There is 3150 downstairs and 1150 upstairs, and we're in the southeast with moderate winters and hot, humid summers. The house is well insulated.

The Square Footage "rule of thumb" is not a good basis for sizing, but the two sizes you've been told are not particularly consistent with the size of your first and second floors. I'd ask to see the load calculations supporting 3 tons for the 1150 sq ft second floor.

Heat pumps are sized for cooling, not heating. If additional heating is needed, this should be as auxiliary heat.

"Variable" is a miss-used term in this business. I take it they mean "inverter"? A two stage system will dehumidify better if that helps your condensation issues in the summer.

Variable is more often than not referring to blower motor of the furnace or Air Handler / Fan coil.

I suppose some techs might stumble and call an inverter condenser a variable unit. It's not that saying that is wrong, just a misuse of terms really.

Two stage isn't really two stage in this realm it's typically 2 speed (the compressor is merely unloaded in first speed). In first speed capacity is generally around 70% of over all capacity of the machine. So while this will do a bit better with dehumidification than single speed unit, it's a bit cheesy how they implement this on most systems via a dead band of usually 3 degrees on the thermostat. If you live in a humid climate you will discover this gimmick really quick. (They were all the rage here about 5-6 years ago, not so much now for people that know better)

With 70% capacity you typically get over cooling as opposed to anything real in the way of dehumidification. It's better than a single speed machine, but not much.

Some inverters do much better because they start low and ramp up. Some machines typically Carrier limit their inverter to 5 speeds. So in that sense they are slightly better than a 2 speed machine.

Other inverters have the ability to adjust in 1% increments, that is the cream of the crop when it comes to better dehumidification. However, there are some gotchya's to be aware of.

All major US manufacturer's will require communication of these inverter machines to operate as designed. The communication is done via proprietary controls, if there ever comes a time down the road these controls are discontinued switching back to a legacy control will for the lack of a better word 'cripple' the machine. Likely similar if you chose a 2 speed option, that may require communication on some units to function fully as MFG intended.

I believe Amana / Daikin have chose a different path and put these control logistics inside the furnace or AH, but it's probably still communicating between AH / Furnace to outdoor condenser. So any thermostat will work with these.

The newcomer Bosch does things differently. They make inverter heat pump with 1% steps up and down, do not require any communication, just a simple regular thermostat of your choosing. However, you shouldn't look at air conditioning as dehumidification control, whether inverter or not. Because these machines still run off temperature. Even with dehumidification settings on a thermostat. Most are dead band of 3 degrees from set point temp.

The inverter machines do a better job at it because of the 1% steps up and down, provided of course the MFG didn't limit that ability like some Carrier models. The reason why 1% steps up and down are important is run time. They will run longer, as long as the machine is running in cooling mode it is dehumidifying. During the warmer months little fuss if installed properly. During shoulder seasons is when you'll see humidity and temperature set points collide shutting the system off. When the system goes off, there is no dehumidification.

The biggest hurdle to Bosch is primarily that it's made in China. That being said... all machines have parts that either come from China or Mexico and are merely assembled here. This is about as non biased as I can be. I have a Bosch Inverter heat pump at my house.

I went thru this decision 2 years ago at my house. I don't regret the decision.

I wondered if 2-stage or variable is preferable and whether one of these brands is preferable over the other? In other words, am I comparing apples to apples here?

I own 2-stage variable speed equipment and I feel it is worth the extra money. The manufacturers take liberties in describing their equipment as "variable". It gets very confusing when shopping for equipment.

Carrier and Bryant are the same equipment. You should be able to find the Carrier equivalent of any Bryant model. The Bryant model line up is not as extensive as Carrier. The same is true for Trane and American Standard. There should be a Trane equivalent to an American Standard model. But I do not believe American Standard makes of the equivalent Trane models. This allows to make apples to apples comparison between Carrier and Bryant, and Trane and American Standard.

All of these brands are considered to be good equipment. Carrier and Bryant offer lower end equipment (Comfort and Legacy). The equivalent to models made by Arcoair, Heil, Tempstar, Comfortmaker, and Day & Night.

The equipment models you have listed so far are all good. The Trane/American Standard heat pumps have on demand defrost. I do not think Carrier/Bryant has this.

The most important thing in all of this is proper installation of the equipment. That includes the proper sizing. You are about to spend a lot of money if you are buying two new systems. You want an installer that will do a proper heating and cooling load calculation.