A two speed AC is more energy efficient, but only slightly. Most two speed air conditioners unload the compressor in 1st stage. Most manufacturer's it's around 70% of capacity of the machine.

When 2nd stage calls, the compressor loads up to 100% of capacity.

Back when these first came out they were all the rage here because there was nothing better. But time changes things and here the better option is Inverter. The compressor in these is fully able to ramp up and down. One such model has over 50 speeds.

Some manufacturers models limit the number of speeds... many ways to do it depending on controls, what the goal is of the manufacturer. When it comes to Carrier brand the inverter realm of theirs gets into proprietary equipment controls and such. Many other manufactures are the same way. So if they stop making the controls... well that doesn't spell anything good for you if you own one.

In terms of efficiency savings? an inverter AC can cut your light bill in half.

I installed an inverter at my home in late 2019. It's not a Carrier brand.

Is an inverter AC for everyone? No. It fully depends on what comfort means to you. There are risks as with anything else.

One risk that effects everything is the new freon phase down. What happened to R22 Freon is now going to happen to R410a. By 2023 for California, other areas probably not much long after that.

Can you post the model numbers of the two quotes and prices? Are you getting gas furnaces or heat pumps?

Two stage equipment is more about comfort than energy savings. There is some energy savings but depending on your climate and usage the saving may be small. If you live in an area with high humidity in the summer, then a 2-stage AC is going to provide better humidity control. In some parts of the country, the higher SEER and EER rating may qualify for a utility or state rebate. This helps bring down the initial cost.