First off if you are unable to find a dealer to perform a load calc, then do it yourself. Cost is minimal. Will take a couple of hours to gather the information. I can provide a link if you are interested, it will make you a better informed homeowner as well.

The AHRI number provided on thecTrane quote is not correct. It shows a 3 ton condenser. Please verify.

And the AHRI numbers on the Rheems do not identify the furnace mdl number. Need that info to give you an informed opinion.

Just on the Trane info alone, I would say that furnace may be oversized.

Any info on new linesets and new air filter cabinet?

On the Trane system, you want a true two stage thermostat. You were not quoted true two stage stat like HW VP IAQ.

Post back with complete and verified info.

IMO

Thank you a lot for the quick response. Please see the reply below:

1. Trane contractor told me this morning that he can do it but need to schedule it. My AC is not working since 9:30am. It will be 95 degree later and we only have fan... We may need to make a decision this afternoon in order that either of the contractors can install the new system tomorrow. Please provide the link. I will try to do it this afternoon. If I cannot, should we go for 5 tons because we may build a small sun room (100 sq ft) on part of patio outside of my breakfast nook (sliding door to patio) 2-3 years later? Rheem contractor thinks installing 5 tons will not hurt the life of the machine because his thermostat will control the on and off, if we concern on oversize issue. Is it true?
2. My bad....The correct AHRI number is 4180435.
3. Rheem furnace model number. This contractor forgot to include the model number in his email. We are waiting for his call back to get this number. The information he provided in the email is: "The furnace is a 80%. The SEER only requires a specific furnace when a variable speed blower is involved. Before you ask, variable speed is worth up to one SEER and is not a very good payoff (more than 10 years)."
4. Trane dealer's reply to oversized furnace is "The XV80 100,000 btu furnace is a 2 stage heat unit that operates at approximately 79,000 btu and 52,000 btu dependant on demand from thermostat."
5. Trane dealer's reply to thermostat is ""Trane" thermostats are manufactured by Honeywell. The TCONT802 is an excellent thermostat and will do everything that you need and at less cost than the HW IAQ."
6. Both dealers are using my existing copper lineset but their quotes include flush of the existing lineset.
7. Yes, we will have new air filter cabinets from both dealers.

I will post the furnace model number within a couple of hours.

Appreciate your reply.

1.You need a load calculation for both heating and cooling

2.the Trane dealer is advising you incorrectly about the thermostat. On a two stage furnace, you want the thermostat to control staging based on demand not the timer on control board that always goes to high stage whether your home requires it or not.

3.lineset whether new or existing must be the correctvsize to manufacturer specs. Close does not count.

4. Why have an oversized furnace whether 2 stage or sgl stage. It will only cost you more to operate. Dumb, dumb, dumb. Size to the load calc.

Sorry to sound so adamant but this is important purchase that should be sized correctly with best equipment including thermostat to take full advantage of equipment's capabilities.

Link for software attached.

IMO
Good Luck

Here is a link that might be useful: HVAC Calc Software

You are better off spending a few nights in a hotel then be rushed into a decision that you will later regret. You want a properly sized unit installed correctly by a reliable contractor. You need a written quote with all the correct model numbers and details of what work will be done.

Rheem furnace model is RGPN, 80% AFUE Single-Stage PSC Motor.

Thanks!

Not as good as the Trane as long as Trane is equipped with the correct true two stage thermostat, not the 802 or 803.

IMO

Rheem model number is RGPM1debrjr. Thank you, everyone, for the inputs.