Medanfen has some major input lag issues and I don’t see this with PS1 emulation, so this seems specific to the Saturn core. I don’t see a similar slowdown in Yabause.
(I’m not an emu dev. Just my experience and what I read)
Saturn games often (though not always) had more input lag than their PS1 counterpart. This apparently happened on hardware as well.
Resident Evil for example lags quite noticeably more on Saturn than on PS1. While Street Fighter Alpha (1) seems on part with PS1.
Likewise, some arcade ports lag quite a bit more on Saturn than on arcade (the Saturn King of Fighters ports for example) while other ports feel pretty much the same. Ex: Sat port of Super Gem Fighters Mini Mix. Maybe one additional frame. Usually, I found Capcom arcade ports are quite good in this regard while SNK’s ports…not so much.
There’s also Saturn exclusive such as SteamGear Mash that feels extremely responsive -almost next frame but most likely 1 frame.
So basically seems it was very dependent on how the games were programmed and optimized and whether or not the devs optimized the processing chain. If they didn’t, then yeah, it could lag quite a bit more than PS1.
All this to say I don’t believe Beetle Saturn adds any significant lag -it can be pretty much on part with hardware, provided the user uses lag reduction options like hard sync on their end of course (there’s also an option in Beetle Saturn called “Mid-frame Input Synchronization” which might help decrease it further but will add an additional CPU cost).