No, this is an area where you can't generalise without knowing the specifics. Firstly you are confusing fault protection with some nebulous concept of "safety". Fault protection has a specific meaning and there are specific requirements. SP and DP devices both fulfil these requirements.
To extend the discussion to safety in general, then you need to look at a wider picture, like can the neutral take on a noticeably different potential to the local earth? For many cases (i.e. TN-C-S / TN-S) the difference between DP and SP is moot, and even with TT it is negligible.
The time that DP device does have a clear advantage is that you can also use it for isolation (something that requires DP switching).