When stochastic screening was introduced there was a lot of discussion of whether this was to be an improvement. So far it was only available for offset-litho printing and in offset-litho the solution of anti-moiré had long proven the different screen angles for the 4 CMYK colours [cyan, magenta, yellow and black] like 75, 15, 0 and 45...
Only a few stamp issueing countries are steadily using a stochastic screen for their offset-litho like Australia and Canada. Other stamp printers hardly ever use that stochastic method unless the artwork they get from the designers is rather poor. And in the latter case using a stochastic screen just flatters it.....
Some examples:
German State Printers:


Swiss Post Office Printers:


Denmark Post Office Printers:


The German and Swiss screens are really stochastic, the Danish one is fake - you can see the horizontal/vertical screen still...