I'm not talking about GamePass with native ports to PlayStation, though. Just cloud versions, and not even for all 1P games. If people want native versions of those games, they would still need to buy an Xbox (or PC). Same if Sony offered a version of Spartacus to Xbox that just had cloud-based versions of most 1P titles in the subscription.
Or in both cases, they could just leave what games are offered to MP-centric titles, multiple bundled into a subscription offering, if they feel they can generate more money from the fanbase by including multiple MP/GaaS titles in their subscription offering on other consoles. And maybe for 1P games not of that ilk, they roll into the subscription for other consoles later down the line.
IMO I think full-fat GamePass on PlayStation would be worst because that sounds like it would necessitate native PS5 ports for games to run on local PS5s, and that would not only hurt subs & sales on Xbox but also complicate the development teams by needing to build/compile native versions for yet another platform specification. From what everyone keeps saying they act as though game streaming is a big no-no for the hardcore/core gamers so people who want the best MS 1P experience are still going to need to buy Xbox or PC hardware.
For the casuals, whom are more accepting of cloud streaming for games, I think that's where you might want to stagger certain 1P offerings of the service on rival platforms, though by that point if they're willing to settle for cloud streaming they probably are a lot more platform-agnostic, so they have less reason to buy a console anyway. MS still gets their sub revenue from them regardless of the platform they're on, if they're using GamePass on PC then they'd only have access to 1P GamePass content and cloud-only versions, otherwise PlayStation is treated the same a a smartphone or tablet in Microsoft's eyes, IMO.
And, all of this would apply to Sony offering a version of Spartacus on Xbox that's just the 1P content offered through cloud-only streaming, too. Potential staggers of selective content parity between PS and non-PS devices, etc.