Trane (American Standard) is obviously one of the top brands in the industry. I've owned their equipment in the past, and found it good from an operational and reliability standpoint. But at the absolute top end of the HVAC food-chain, I myself happen to prefer Carrier and Lennox (with York in line with Trane). But you wouldn't be making any mistake buying Trane, particularly if you had a history with the installer/dealer.
Meanwhile, Maytag is a brand name from suburban St Louis manufacturer Nortek (formerly Nordyne, until JAN 2015). Nordyne had been well-known for consolidating traditional brand names like Broan, Frigidaire, Gibson, Kelvinator, Philco, and Tappan......and then slapping them on the nameplates of mechanically-identical residential HVAC equipment. Carrier does something similar with their Bryant and Payne brands......American Standard with their Trane and American Standard brands......York with their Luxaire and Fraser Johnson brands......and Lennox with their Armstrong Air brand. My impression has always been that Nordyne quality meets the industry-standard; so for the right price......which should typically be comfortably below the majors......I consider them a fairly safe choice in their own right.
Trane traditionally used their own orange-colored "Climatuff" compressor (not sure that's true anymore); though I'm fairly sure these are/were always traditional Copeland reciprocating designs built exclusively for Trane. Most everyone else in the industry (including Carrier and Lennox and York and Nordyne) uses the black Copeland branded pump. I don't know if Copeland builds their more efficient scroll compressor for Trane under the Climatuff name; your dealer should know (that is, if you're interested).
All US manufacturers use components (compressors, fans, metals, electronics, etc) from the same suppliers. That said, I (and we) used to sell the exact same reversing valve.....the device which makes a heat pump, well, a heat pump......to Carrier, Goodman, Inter City Products (Arcoaire, Comfortmaker, Heil, Tempstar), Lennox, Nordyne, Trane, and York. However, the more premium models of a given brand name offer features/functionality (and efficiencies) that mid-lower models don't.
You're paying largely for advertising.....and to a lesser extent, features......when you buy top-of-the-line (though the newest industry technological developments will tend to originate with the majors).. Don't underestimate the value of a strong dealer; especially one with which you have a history. Don't forget, he's the one who has to run warranty calls on the system; and he doesn't want to come out "for free" (though he is reimbursed by the factory for warranty work) anymore than you want your new System to breakdown. After all, that warranty call is time his guy could be out installing a fully-quoted new installation at much higher profit.
Speaking of warranties......pay very close attention to them for each make; ideally, you'd like them to be as comparable as possible between the proposed systems (and don't forget, the longer warranty is a function of the cost of the System). In this case, if the warranties of the Maytag and Trane units are the same......and you feel good about the Maytag dealer......that's generally a good enough reason to save the money and buy the Maytag. OTOH, if the Trane dealer was more professional, and earned your confidence through their proposal and presentation, that represents its own kind of value......and could be indicative of how they run their business versus the Maytag dealer.
