I don't know about the Orloj, but the undisputedly most precise mechanical clock in existence today is Jens Olsen's World Clock in Copenhagen Town Hall. Horological porn. An engineering and manufacturing marvel &c.
I had a hard time finding exact accuracy stats for it online, but in a book I have on it, published when the clock was finished in the fifties, it was stated that it was expected to be no more than a couple of seconds out in a thousand years.
It tracks every astronomical event you've heard of and quite a few of which you haven't.
I also couldn’t find accuracy stats online or any form of explanation of how it is so accurate. The Copenhagen museum states that only atomic clocks are more accurate than the Jens Olsen clock, but there is no support for the claim.
For a mechanical clock that needs to be wound once week I find it hard to believe it is more accurate than a high accuracy quartz with plus minus 10 seconds a year.
One thing that I didn't see mentioned, which I think would be pretty cool to know, is how accurate is it (e.g.: quartz versus atomic)?