Well yeah, in-universe the Prime Universe Stardate system makes more sense.
I think it would be a system that would have to take into relativistic effects - not just for speed, but also that fact that time runs differently in different gravity wells vs. flat space, orbit vs. ground - and even with FTL travel...well, according to Einstein, traveling FTL would mean traveling *back* in time. I'm sure that in the Trek Universe that doesn't happen, of course...but all in all, well, really....there isn't a universial time that every observer would agree with. But Stardates are a way to take that into account, and try to formulate some kinda of date system that everyone can sort of agree on - and that takes into account relativity and such and clocks running at different times.
As such, it would be an immensly complicated dating system! Probably take a computer to sort it all out.
I think the key to how it works is in the name - "Stardate" - probably ti takes into account to positions of stars - and probably uses some sort of pulsar map, as well as Federation/Starfleet subspace transponders with atomic clocks (or "quantum clocks") and such.