PS3 was a complete disaster for Sony. Just looking at LTD console sales really doesn't cut it here lmao. The rest of your analysis seems solid though.
Yes, PS3 and specially its launch was a total mess:
-Relased way later than MS specially on the main PS market
-Priced way too high
-It was even way more expensive to produce it, causing massive sales to Sony
-Launch line-up featturing the popular giant enemy crab and no big hits
-Extraterrestial hardware and tools, super difficult to use for dev
-Forced gyroscope motion controls as the only control in some launch window games ruining stuff like Motorstorm (later patched to allow proper controls) or Lair
-3rd parties started to go multi due to rising dev costs, and instead of money hatting GTA, FF, Devil May Cry or Tekken to stay, they moneyhatted crap like Lair, Haze and PS Move crap and even created a 'metaverse'
They were lucky that later they kept fixing many of these issues and they started to get many amazing exclusives like LBP, Killzone, Uncharted or TLOU series, and that we the Europeans bought whatever they made. Here even the PS4 at 599€ and the PSVita performed well.
Current gen is different. Neither is competing against each other anymore. Ps5 hardware sales is useless against xbox, because of the day1 pc sales. Its useless, because of the xcloud. You could say, xbox went above, and joined new realm with these 2 options.
They will continue being direct competitors, but even after the Zenimax and Activision acquisitions will continue making less revenue than Sony. Specially considering Bethesda and Activision Blizzard games will drop their revenue due to many of their copies of new games being included in GP at launch instead of being sold at full price, and will drop even more if they decide to keep some big Zenimax/ABK game out of PS.
Their game subscriptions will become more similar to each other and will fight harder to see who gets what there. MS already invested hard on mobile with Minecraft, King and CoD Mobile, and Sony bought the dev that makes their only mobile game, but that generates over $1B/year and will continue buying big mobile stuff. I think MS will be more dominant on more neutral territories like PC and mobile where they area diluted between many other players while Sony will be more dominant on consoles (hardware sales, total game sales, exclusive sales, average metacritic or awards etc), game subscriptions and VR.
Even Jack Tretton, who ran SCEA at the time, compared taking over Sony in that generation to being the captain of the Titanic.
It's funny to see people from USA talking as if USA is the world, or as if the rest of the world -or the rest of America- wouldn't exist. He only was in charge of a regional division of SCE, not the whole SCE, PlayStation or Sony. USA isn't the world, it was less than a third of the market for Sony. Their hardware sales heroes who saved the crap selling a shit ton of consoles were the European ones, commanded there by a guy called Jim Ryan. Jack sadly left the ship, Jim got promoted to CEO of SIE.