These furnaces are all essentially in the same class of furnaces 96% condensing, 2 stage, variable speed blower or ECM. Communciating if proprietary thermostat of the particular brand is chosen as the control. (The mfgs reliably just copy one another more or less)

Other differences can be control options (proprietary controls for specific brand, model etc) Algorithm chosen to control the machine.

Product Warranty: More or less the same if the product is properly registered, properly installed etc.

The primary difference is sizing as the Carrier you list is an 80K BTU as opposed to 60K BTU from the other choices (Lennox & York).

I don't know specifically what size the Carrier is because the model number you provide is redacted that would include that info. You list it as an 80K BTU furnace.

If you need the 80K BTU then the Carrier would be the better choice of the three.

If your current furnace size is 60K BTU the duct work is probably sized for 60K BTU. The difference is about 400 CFM of air on high speed and 300 CFM of air on low speed for the Carrier furnace.

So undersized duct work can cause a myriad list of problems. This is why installation is typically the most important part of the job.

Other considerations: maintenance and equipment repair support. It's not just about choosing a brand, it's also about choosing who you'll call when you need maintenance performed and or repairs.

What is my favorite brand? One that is broken. They all break... some brands more than others and most of the time the installation of the machine was the biggest factor among them all.

Out of all these I really have no preference if sizing and ductwork and installation is properly done it really doesn't matter which brand. The brand debate is mostly an illusion at this stage of the game.

Some locations are better suited to one brand over the other due to distribution logistics. Meaning the ability to get "specific" parts in a timely manner. All of these brands contain parts made in remote parts of the world. (Meaning outside USA / Canada)

I service the Katy, Texas area.