One of the things I miss from the Japanese side were the silly interactions you can get from things like having a Puso Ni Comi watch party when the television screens streamed an episode and players would start sharing the keyword at the end of the episode. The Japanese version was shamelessly a commercial for games/collaborations that were related in some way because I distinctly remember Persona 3 and 5's Dancing games having numerous commercials playing on the screens (the trailers, the commercials, and then later the concerts) because those games were "new" and had not yet been released. I was surprised to see that in the global version we at least got the concerts and the scratches even without their original context. Alongside this there were things like celebrity appearances (such as Sachiko Kobayashi making a guest apperance) and live concerts for the players who were able to attend conventions/live events regarding Phantasy Star Online 2. It was "more" than just a game over there and I feel that Puso Ni Comi has a decent grasp of showing that - whereas on our end what we have on global is largely a compromise of what Sega is still capable of sharing and pulling off without getting too deep into licensing and digging through their web of older content that the Japanese version no longer plays with.
Even for new players of the Japanese version (at least to my knowledge), those who joined after the removal of the Omnibus are unable to access the Event Chronicle that was full of scenes from the Matterboard/Omnibus days which have been largely cut out of the game and effectively turned into "Deleted Scenes." I would love for this to have some how been accessible for global players especially for people who wanted to see more of the Episode 1-3 story and world. Like what was said, Sega has no issues with deleting data in the game when the content is no longer relevant (such as the Elzelion fight from the Monster Hunter Frontier Z collaboration being completely inaccessible despite Extra Hard Explorations for the relevant areas still being accessible and the Neon Genesis Evangelion Emergency Quests being completely removed though I do not know if the story-related cutscenes are still available to see). I am hopeful for Sword Art Online potentially showing up if only because it is a relatively popular series and that the collaboration was recent but I lean on the side that unfortunately sees it as "unlikely" for the time being.
Even despite all that, the global version fixes some of the most glaring issues on the Japanese side that I see which could be simply expressed as "convenience." The Japanese version still does not allow you to freely run Trigger Quests of just about any fight in the game because there is no badge shop yet that hands those out and the game is full of drops and older content that may or may not be relevant or even tradable anymore but you still have access to getting all of that in some way. There is a very big "graveyard" of equipment you just simply have for nostalgia or for Transmutation fodder due to there being the presence of so many mechanics that have since been powercreeped due to the vertical progression the game has taken especially during Episode 4 with the introduction of New-Type weapons. In the global version as far as I know there are no level-caps and there is no complete restriction to the game's schedule if you wanted to go and fight a big boss. Because your pool of equipment in general is smaller it is easier to focus on what to get (and even easier if you already keep up with the current campaigns) so I feel that the Global version is definitely easier to jump into while still potentially overwhelming. The Japanese version is definitely further along in that new players can get further and faster but because the global version is so close the only real glaring difference I would point out in terms of sheer equipment is the fact that we never have gotten replacements for the all-class Katana with Morning Mistreaver baked into it (it is essential for Endless Quests and Time Attacks) and the older sorts of PP Batteries where you can simply stand in place and they work but the Genon weapons are faster if you can deal with the self-damage. This does not get into things that the global version has never really had access to such as Receptors that facilitate making affixing much simpler either or the variety of equipment the Japanese version still has due to PSO2es having its own offerings that carry over and can be relevant.
If it is anything, I still would have loved to have seen PSO2es in some way just to help global players flesh out more of the world of Oracle so we can see the sidestory that took place (even if it wasn't great) and so Sega has a reason to bring more of the PSO2es characters and cosmetics as guests and hosts for events. We had an IDOLA scratch recently but both PSO2es not being present and IDOLA not having any link to the main game unfortunately pushes these two games into being very far-off islands for Phantasy Star Online 2 so the global version comes off to me as a much smaller scale of a game than it is in the Japanese side of things. Admittedly, I would also love to be able to get the cosmetics related to the side-material such as the Phantasy Star Online 2 Trading Card Game (you can exchange for a literal Duel Disk camo for the Talis if you did not find one as an Old-Type weapon).
In terms of the playerbase I would definitely say that Ship 2 on the Global version is effectively a more "condensed" version of Ship 2 from the Japanese version. On the Japanese version it wasn't uncommon to see someone use the "Good Job" or "Kudos" mechanic to fling insults to one another as I used to get harassing messages due to my class and playstyle at the time (Hero during Episode 5 when the Black Dragon/Black Fellwyrm had an incapacitation limit and because no one died but I was the player who had 1 HP at the end). The playerbase was generally quiet especially with the Japanese players but this is largely because the Japanese players flock to their forums and messaging boards to dox players they dislike or gossip about players elsewhere. Us not being able to read it without translations does not mean this didn't happen but it definitely makes sense as to why on these forums naming players and attempting to start witch hunts is frowned upon. In additional what I had mentioned, the content on the Japanese side was much harder than it is on global largely because on the global version Sega has gone through to both simplify content and provide the means to pass content (Millionaire/Croesus weapons available day one on Episode 6) whereas the Japanese version had to take nearly a year of Episode 5 equipment becoming weaker and weaker to Episode 6 content. It was not until much later that thirteen-star units were introduced and even later that older weapons were given "Redux" or "Plus" potentials to bring them up to par with higher-end Episode 5 weapons or later on higher-end Episode 6 weapons. I feel this can be subjective because the harder progression definitely can contribute to the need of having Expert Matching when you wanted players to at least be competent in a party. In the global version I feel at the very minimum you should have Millionaire/Croesus or even the Orb weapons if you are of a sufficient level to wield them unless you have a special class combination that prevents you from doing so (such as Techer/Ranger and Fighter/Bouncer).
In a nutshell through the wall of text I have created, I feel that there are significant differences between the Japanese version and the Global version but it is not "tragically different" that the games are foreign to one another or that they should not be considered "Phantasy Star Online 2." Instead, I would see it as rather you can see it almost as though how parents choose to raise their first child compared to their second child who is very similar but not quite the same. To me the global version is still largely the same game with a lot of its fluff (including the fun fluff) lopped off but I am hopeful that at some point my friends on the global version can experience what Japanese players got to experience or that with New Genesis things are evened out and tighter between regions (hopefully closer to the Japanese side than it is to the Global side if I had to lean in any direction).