Seen lead dogs do all the above.
I have two that absolutely hate each other. Put them together an the fight is on. But in the woods I run them together because they push each other.
Saw another that will hunt its rear off by himself or with a lesser dog..but an equal or better dog they will sull up like a dang women and do little of nothing.
Have another one that isn't alpha and isn't lead...but will break off and do his own thing regardless to what's happening.
I say dogs are exactly like people. You have all types of individual personalities that come into play that ultimately make good dogs. But you really can't compare them do to their own weird quirks and demeanors.
Find out what way your individual dogs performs at his best and keep it that way. And I agree the best of the best are gonna do it anywhere anytime no questions...but I bet they have an identifiable oddity.
