Thermostat and Dehumidification

I'm looking at a replacement HVAC system and I have narrowed it down to two local companies even though they sell different brands. Each company is quoting a variable speed, two-stage furnace with a single-stage A/C compressor. One company is telling me that I can use my existing newly installed Ecobee thermostat while the other states I need to replace it with one made for the system. Variable speed blowers are new to me and seem to make sense with the heating side of things but I'm having trouble wrapping my head around the variable speed blower and a single-stage A/C. Dehumidification is just over cooling to help lower the humidity in the house? On a variable speed blower, is the blower speed controlled through the thermostat or through the furnace control board?

Could anyone help shed some light on this or point me to a resource online to read up about it?

Thanks,

source https://hvac-talk.com/vbb/threads/2240051-Thermostat-and-Dehumidification?goto=newpost