Here in Austria its completely up to the controller how to use the 3nm sep; outcome has to be 3nm or 1000ft, no matter how.
That doesn't mean everyone here is pushing his/hers adrenaline by letting 3.1nm happen with a/c almost opposite or sharply crossing, but it surely is handy at almost parallel SIDs which are still close to each other (must be bloody inconvenient to assign headings to a/c on parallel tracks, one overtaking the other with min sep of 4,5nm when staying on the sid).
What's the real advantage of headings vs planned route? Don't mistake me, I love headings and use them whenever things take a closer look.
One argument I heard often is wx-deviations. Well, I sure count on any a/c to report any deviation, as is required (flight planned route doesn't allow for any deviation without reporting, at least in my FIR; same with heading)
Below the line I should feel even better when letting 3.1nm happen on flight planned route, because that is what is tracked. A heading's track might change when descending/climbing because of different wind.