I'll bite, because this actually turns out to be a pretty interesting question.
First, let me link an
interesting interview stumbled across while trying to figure out where Atari got their ASICs fabbed.
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I wasn't able to find a straight answer for that, actually (apparently at least one rev of the 2600 TIA bears a 'S' marking, who was that?), so I'll try not to weigh that too heavily in the rampant speculation to follow.
First, ground rules: Let's assume Jay got a green light to assemble his own independent project group to work on a multitasking computer capable of 'simulation-grade' graphics, resulting in a chipset similar to Lorraine.
Fact is, if conditions had been favorable, this could have worked out a lot better for both Atari and Commodore.
First, Atari:
If Jay proceeded at Atari, the team would've been a bit different, and software certainly couldn't help but be different. In the end, many of the same compromises would have to be made -- RAM was stratospherically expensive, the biggest constraint on any design of the era -- but a lot of time pressure would've been taken off the OS team.
I believe Atari would've needed a solid fab partner or its own fab to produce the chipset for any use, and the nature of that deal would have had rather huge repercussions in the industry, especially in relation to MOS as supplier for the 8-bit world.
There would've been what, in retrospect, we can see would have been a major difference propagated through the resulting machine:
Graphics at 400 lines NI would have been supported in the first model; Atari didn't have quite the same concerns with sourcing monitors as Commodore did, and if the project were greenlit as a computer (requisite to keeping Jay there), it would've been accepted from day one.
In relation to this, monochrome monitors were relatively cheap at the time, and if the machine was capable of a crisp high-res display, they probably would've been the choice of many early-adopters.
With either display, it would have been more expensive. It would likely have been more 'complete' at release time, assuming all the QC processes of a healthy Atari were brought to bear. This would have made it very obviously a 'serious workstation,' while the same chips would rapidly be repurposed into coin-op hardware and, perhaps, larger stuff for the low end of the simulation market.
Atari marketing would've had as hard a time with it as Commodore's did in our universe, but the slightly more complete machine would probably have been an easier sell to certain markets (CAD, etc). In the US, despite being a 'games company,' Atari also had wide recognition (via the 2600) as a 'big' national brand that, like Disney, might
potentially have the resources to diversify into 'serious' fields... in contrast, even through the C64's success, nobody ever quite knew what to make of Commodore.
Atari had already started thinking about compatibility (at least between peripherals), something Commodore was still struggling with.
Atari would have had no more prejudice than Commodore at selling a sub-$1,000 model once that became feasible, something that would've put the likes of IBM and Apple on higher notice in a machine that bore more resemblance to products made by them. (The resolution issue always made the Amiga look a little weird, frankly, especially in comparisons -- look at ArsTechnica's attempt at a Commodore-style comparison ad between the IBM PC, Mac, and A1000; while the capabilities are there, the display is half the DPI of the competition, even when the competition only had a character generator.)
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Commodore, in the meantime, wouldn't have had anyone to 'rescue,' probably would've seen the CBM 900 or something like it to market, and together with the LCD could have had an interesting business system worthy of their full name. They probably would've found a more-than-modest success in the UNIX market, with its own interesting repercussions. The 8-bit line would've probably carried on, culminating in something like the C65 -- probably with more 'smart terminal' functionality built in, and Jack probably would've felt some cognitive dissonance until he could actually unify the big server machines (for the 'classes') with the next low-cost designs (for the 'masses').
Figure a 'reverse NT' situation, with an Amigaless Commodore releasing a next-wave single-user home machine for the early '90s, perhaps learning to monetize MOS and pick up free rights to interesting third-party silicon in the process. Depending what CPU won out, this might've forced MS into interesting contortions, trying to stretch Windows onto that platform as well as the Alpha. Also figure Tramiel, were he still at the helm, to see the potential in the Internet through exposure to the UNIX market, and push for it to be well-supported... It's very hard to say what Commodores would've looked like by then, but they might've encompassed a niche between WebTV and the iMac.
Where Atari would be by then, what 3D gaming would do, and what (likely small) percentage of the market they'd retain... who knows? At least they would've been in a position to adapt circa 1994, instead of already being doomed.