I had my third daughter last April here in Zurich at Unispital (on basic insurance). You should know that there's a bit of a baby boom going on here, and though they won't refuse you, Unispital did have days last year where they were forced to send women out to Winterthur
In any case, it isn't dependent on when you register with the hospital, in agreement with what has been stated on this thread. However, it is worth asking around at different hospitals, since I was specifically told that the Zurich city hospitals don't coordinate with each other, so over a period of weeks Unispital could be very busy and Triemli could be nearly empty.
One good thing about having a busy hospital-you may get bumped up to the half-private recovery ward (Wochenbett)