It depends on the writer.
I always saw the Phantom Stranger as being cosmically aware of things, things that could happen or will happen and makes his plans accordingly. Pre-Nu52 I also interpreted him as immune to all the timeline/universe altering events. Whereas the Spectre is just ludicrously destructive.
I've read some stories where he is an agent of the Lords of Order and Chaos then others where he is an agent of the Big G himself. When did the switch up happen.