Depends upon your service agreement and requirements. If your service method can be executed by any requestor, select stateless.

But if your service method needs a requestor which already has a state and clipboard data (object content) and has completed calling one of the service method beloning to the same package, then select stateful.Basically stateful is useful when you are expecting a sequence of calls for a particular transaction or person. ex : update the employee address,salary and leave details. Advantage of stateful is the time saved in Authentication as the requestor is only authenticated once and the data in the requestor.

Remember to select the End requestor when done?  on the service method when stateful is selected to destroy the requestor once your stateful set of service methods are finished.

Hope this answers few basics.

https://pdn.pega.com/integration/comparing-stateful-and-stateless-servi…

Thanks,

Ashok