Side discharges are nice, smaller footprint and can be mounted inches from the wall, probably will be quieter also, not sure who makes the HMH7, thinking it’s made/manufactured 100% in China. York could easily have a partnership with another manufacturer to supply those.
The YH2F is your traditional configuration vertical discharge. Says the SEER2 is 15.2 and EER2 11.7 and HSPF2 8.1 if your into efficiency ratings. Those numbers are not real world but are probably close, as of 1/23 the rating figures were changed to match a more real world install. Used to be just the SEER, EER and HSPF.
Looks to show for a AHRI ( Air Conditioning, Heating and Refrigeration Institute ) match for the HMH7 the indoor section needs to be a 5 ton Air Handler, looks to show SEER2 of 18
Certainly the HMH7 is a more complicated system with probably more proprietary parts. Hopefully the bidding Contractor has added training and install and setup and sizing many already to have a good handle on proper installation. May want to consider a surge protection device for that model as it will have more electronics than a single and two stage system.
Make sure to register your system as manufacturers warranty decreases if system never gets registered.
What is the labor warranty this Contractor is offering, if your interested more than a basic one year, manufacturer also offer extended labor warranties. Typically it will be either five or ten years. York along with Daikin are the only two manufacturers that backs their extended labor warranties. The other big names like Carrier, Trane and Lennox, Rheem etc. use a 3rd party to back their extended labor warranty.
If you’re proactive on your new system, ask them to explain the sequence of operation to you before handing over the last payment. Things like what happens to the outdoor unit and indoor unit when it’s near the thermostat setpoint and when the system is further from the thermostat setpoint. What and how does the defrost work, what initiates and terminates a defrost. Are you having electric heat strips installed? if so how do they work when system is in defrost. Is it hooked up to come on?