Xbox wasn't out during the PS1, but i'll assume that was a typo, it happens. I had a Dreamcast over a Ps2 which was a superior experience, although it is subjective.
Xbox 360 launched first, cheaper and had games playable before PS3, because it launched first. The Xbox 360 was widely accepted as the better console for the first few years of the gen. Around 2008 or 2010 depending on your preference, Sony reduced the cost of the Ps3 and started releasing technically superior games. Uncharted (2?) blew Gears 3 (which had the best graphics on xbox 360 to that point) away by a land slide.
It's not a dream of an xbox come back. They can still come back, even if they choose not to or don't have the skills to do so. Atari and Sega faced the same fate.
Hate to say it but at least for the rest of this gen, especially if Starfield underperforms, there is no magical Xbox comeback. Sony has ridiculously good momentum, and Nintendo's holding in strongly themselves, and will undoubtedly see renewed momentum when the next Switch is revealed. Microsoft are kind of just sandwiched in the market and provide no unique value relative Sony or Nintendo that actually resonates with the wider market.
When Sony were down momentarily with PS3, they still had more market relevance and brand power than Microsoft had when the XBO began lagging behind, or the Xbox Series have today. The market was also a lot different back then so it was relatively easier in ways for Sony to come back with PS3 than it would be for Microsoft to do the same. And, unlike Sony, Microsoft have a much longer track record of sustained disappointments, going back to at least 2016, but cracks were showing even as early as 2010 after Kinect released on the 360. They just didn't really get noticed at the time because of 360's strong momentum from 2005 - 2009 and Sony only having just began their comeback with PS3 (and they had a big setback with the PSN hack of 2011).
Conversely in terms of the wider market Sony's only period where people were seriously disappointed in their performance was 2006 - 2008, just a couple years or so, and things started turning around from 2009 onwards, never having any major momentum drops (tho again, some momentary road bumps like the PSN hack). MS's track record with general market disappointment has been much longer so it will be magnitudes tougher for them to overcome it and have a proper comeback that the wider market actually responds to.
The only thing currently giving
any hope that Microsoft could potentially have a comeback (while sticking to the regular console business model) is their sheer amount of income flow. Which could stave off Xbox losses in the meantime because Xbox means little to MS's bottom line. Sega and Atari never had the same privilege of deep pockets, but I would argue Sega in particular gave a much better attempt at a real comeback with Dreamcast than Microsoft ever did in the last years of XBO or are doing today with Xbox Series, they just ran out of money to keep going with the system.
Otherwise, and again IMO if Starfield isn't a bonafide hit commercially & critically, and doesn't do enough to instill some real hope into the future of Xbox 1P AAA releases going forward...then the means of a comeback for the brand can probably only be done by completely removing it out of the space/context of the "console war". Shifting Xbox hardware more into the PC space, opening it up to Windows, and fully bringing Xbox back to Direct X, the way it was meant to bring Direct X to the living room in the 2000s. Well the living room war has been over because there's virtually little chance Xbox can ever gain majority mindshare or market share over Sony & PlayStation, but they can still solidify the PC gaming front that Valve wants to shift away from Windows anyway, so why not use Xbox to do that?
The Cell sucked and was pretty much what fucked the PS3. Had Sony just gone with some basic design like the 360 the PS3 would've sold about as much as the PS4. Sony was never able to match prices with the 360, a few years into the gen and you had a $199 360 and even by the end of the gen the PS3 never reached those prices.
It was the perfect storm for MS and all they managed was to end up in last place and completely nuke their internal studios out of existence. Absolutely no vision.
The Kinect ended up fucking MS later on but during the 360 gen it actually considerably boosted their sales.
Miss me with the arrogant Sony talk, MS has been arrogant for decades and hasn't done shit. Sony fucked up with the PS3 hardware and that's about it, they turned things around within 3 years and set up what would become more than a decade of complete dominance. It's not like Sony planed for the PS3 to not justify it's price, the expectation was to release a premium console that would perform that way.
I disagree that the Cell sucked; in fact it's because of Cell why the 360 even had the CPU it did because some IBM people told them about what they, Sony & Toshiba were working on, and MS wanted a variant of that.
What
actually sucked with PS3 was the GPU. They did want to use two Cells originally; one for a CPU and the other for a GPU, but at some point Sony realized that wasn't going to be feasible. However it was too late to go with a custom GPU design so they had to pick something Nvidia already had on offer and just "make it work". The GPU in PS3 being so modest for the time (IIRC it didn't even have programmable shaders) is why we saw devs (especially 1P) leverage the Cell to speed up GPU operations, and we got some beautiful results out of that.
UC2 & 3, TLOU, GT6...there isn't a single 360 game I can think of with visuals at their level and it's not just because Sony probably afforded those games bigger budgets. The Cell had a lot to do with it, too. PS3's GPU being weak was actually the 360's saving grace in terms of having a performance edge; the "segmented memory" stuff about PS3 isn't actually that true (the RSX could access the XDR memory of the Cell, but had to go through the Cell to access it (the Cell also set up some of the graphics pipeline so naturally the RSX would need to access the XDR memory there), and I think that bus was narrower than the one for the GDDR3 the RSX itself had access to.
If the PS3's GPU was on the level of 360's that generation would have eventually taken a really bad turn for Xbox before the Kinect came out, because 3P performance would have been at parity between it and 360 if not better in PS3's case, and that's before really tapping into the Cell for its own benefits graphics-wise. 360 probably would not have held out long enough in that scenario to get the 2nd gust of wind the Kinect afforded it, as 3P support would have been a lot more favorable towards PS3 in the 2008 - 2009 time frame, and that would have been combined with Sony's 1P hits.