Is there a way to tell what stage the Trane 20i two stage heat pump is operating from the Trane XL900 Thermostat?

tedkat you may and I emphasize may achieve better floor to floor temp constancy with a two stg condenser running on low stage for longer run times. However, I believe floor to floor temp constancy is more a function of good insulation qualities and properly sized ductwork design both supplies and particularly adequate returns. IMO

Heat pumps need to be sized for their cooling loads. If you don't then the equipment will run in short cycles during the summer. This means higher humidity, higher electricity bills, and a shorter life span. Over sized 2-stage equipment is a little more forgiving, but in the low stage most 2-stage equipment operates at 70-75% of total capacity. How do you currently heat your house? If it is fuel oil, then a dual fuel system makes a lot of sense. If it natural gas, then you may not be saving much money with a heat pump. Post the rates of your fossil fuel and electricity and a calculation can be done to compare the relative operating costs.

A 16 SEER heat pump usually has one two-stage compressor. The first stage is usually 75% (approximately) of the rated tons. The second stage runs at the full compressor rating. Not sure about the 18 SEER Amana. The Trane XL19i has 2 separate compressors. The first compressor runs at 50% of the rated tonnage and the second compressor runs at the full rated tonnage. In this set-up, one or the other compressor is running (not both). Just because the heat pumps are rated at 16 or 18 SEER does not mean that the system is rated at that SEER. The matching air handler/furnace is critical in maintaining that SEER rating. An air handler/furnace can decrease SEER, increase SEER, or support the SEER rating. This is why it is important to know thw model numbers of both the condenser (outside unit) and air handler and a/c coil if there is a furnace involved. A heat pump with either a two-stage compressor or dual compressors has 2 stage cooling. If the same heat pump has auxillary heat in the air handler (back-up electric strips, gas furnace, etc), it has 3 stage heating. FYI, you don't necessarily reduce your utility bill with a 19 SEER as compared to a 14 SEER. The Energy Efficiency Ratio (EER) determines your true operating costs, not SEER.