An example - look at the tables for Tpd from SRCK to Qa-h.
LS595, max is 18/25nS for High & low outputs
HC595, max is 40nS.
With 16 MHz clock of 62.5nS the slower part works.
With 32MHZ clock of 31.25nS, the slower part would not.
So choice of part depends on situation.