2 generations ago 360 had a better start because they released the console like a year an a half before Sony, did many things right and Sony had an awful start with many huge mistakes. Even considering that, PS3 managed to outsell worldwide 360 at the end of the generation in a close fight, and if we align sales we see PS3's job wasn't that bad even at the start of the generation.
But outside that, looking at worldwide sales PS always has been way more popular than the other home consoles. They clearly dominated with PS4, PS1 and specially PS2. For what we know in the official announcements and patents or even rumors/leaks, they seem to be doing their job properly, and with that I mean that they aren't/won't make huge mistakes as they did with the PS3 launch.
In the MS conferences I saw they are improving a lot in terms of their strategy focus (games+gamepass) and quality, quantity and diversity of their portfolio. But I have the impression that they are still far behind Sony, and that we'll start seriously noticing the results of their recent efforts in late 2022/early 2023, once they start to release many of the cool looking nextgen only games announced in the MS stream, once Game Pass will have a way bigger userbase and library, and once xCloud is implemented worldwide, with an insane catalog (your entire library and not the Game Pass games only) and once 5G and 4K/120fps tvs achieve a good enough install base worldwide.
So I think it's super likely that PS5 will dominate the generation again as we can guess by looking at the current gen install base, lessons from past generations or data from these videos and related social media posts. As of now, I think the PS5 interest compared to Series X is at least way above the current 2x/2.5x console install base difference.
Specially because of the ~1st year catalog (let's count the last month and a half of 2020 and the entire 2021): MS the bigger weapon has a 4K60fps Halo but it doesn't look as good as many desired, and seems it will have a GaaS focus that I think many won't like. In the other side, Sony will very likely release in that period Spiderman, Horizon 2, Ratchet or Demon's Souls. As usual, Sony's approach is more focused in having more quantity and diversity: these games separatedly will sell less than Halo, but combined will sell more. They try to appeal a bigger diversity of player types/niches, which results on getting a bigger userbase.
Maybe some people love Spiderman and don't care about Ratchet or the opposite. Maybe some people love Horizon 2 and don't care about Demon's Souls and the opposite But all of them will get this console and probably it will be their own GOTY, while in Xbox this will be more focused on a more limited amount of games, this time mostly Halo.