A couple of things. The Fairfield is actually going to come from one of its marketplace partners (who I am unfamiliar with, and thus unfamiliar with their packaging) and it's going to cost you $50 to ship, There goes $50 of the price difference. The Ultimate has the Power Gravity flush, which works quite well. (The UltraMax, which costs more, has the G-Max flush, which arguably is a little more powerful, but the fact is that the Ultimate is a little quieter and was among the best-performing toilets anywhere when it came out, and still holds its own against virtually all competitors.)
The guys have summarized the benefits of buying the Toto: great flush, great-looking, made from better clay, excellent quality control, excellent quality, built to last, simple to fix, parts available everywhere.
Particularly if you are buying online, you don't want to buy something that may be defective, because of the hassle of returning it. There are some inherent risks in getting something shipped to you, you don't want to add to this risk the not-insignificant risk that the AS product sent to you will be defective -- and sometimes shockingly-so, like was the quality-control guy on siesta when the thing came down the line? -- wholly apart from any damage in shipping.)
I have seen too many ridiculously-defective AS products posted on here to have any confidence in them, whether buying them online or at a big box store (from where we have seen defective AS toilet after defective AS toilet).
Oh, yeah. The Toto soft-close seat -- the SS114 -- is the same one used on its top of the line toilets. It's a seat that people who don't have Totos buy because they like it so much. You're not going to be able to say the same thing about the seat that comes on the AS.
One more thing. Both toilets have 3" flush valves, to get more water moving into the flush faster. However, the Toto has a 2-1/8" fully-glazed trapway, which actually makes a difference over the trapway in the Fairfield in terms of reduced clogging. Moreover, in looking at the sketch of the Fairfield trapway, it doesn't look to me as if it has a double-siphon design, nor that it's entirely-sensible based on the criteria that I have seen Terry articulate as to what makes a good trapway. The double-siphon was something first initiated by Toto in the Power Gravity toilets, and explained by an engineer in another post on this board. The double-siphon allows the trapway to forcefully-yet-quietly "pull" the water and waste from the toilet bowl. You'll see that when you hit the flush lever, the thing basically just goes "slurp" as it pulls the waste from the bowl, then goes "gurgle, gurgle, gurgle", then it's done. The first time I used a Toto Ultimate, in Le Pavillon Hotel in New Orleans, I was amazed; it almost seemed as if a trap door opened and the waste quietly fell out. "That's IT?" I thought. How weird. I ended up flushing the thing about 20 times that trip. It almost seemed as if it shouldn't work because instead of the draining-swimming-pools I was used to, with all the attendant swirling and drama, this thing just quietly went "Slurp." And that's entirely-due to the trapway design. There's actually more drama in the G-Max flush than in the one on the Ultimate, which continues to impress me.
As to things like the fill valve, the AS appears to be using a Fluidmaster 400A fill valve and the Toto will likely use a Korky 528 fill valve. The Korky is quieter and easier to fix down the line, but both valves do the job. I myself now have 6 of 7 toilets with the Korky fill valve, either because they came with it from Toto or because when I rehabbed the toilet, I installed the proper 528 (it comes in a few flavors, based on age and design of toilet). But both do the job, so that isn't a factor in your decision. On the flush valve, the Toto is going to use a Korky "Fits Toto" Power Gravity flapper, which you can get almost anywhere or replace with a universal Korky 3" flapper when the time comes. The AS appears to have a fluidmaster flapper, which a lot of folks on here hate, but it shouldn't be a big deal to find a replacement (although maybe not as easy as the Korky). Again, probably not a deciding factor.