Hi
It depends what you're after. In six days you can do both (flying in between the two), however, having travelled across Vietnam I would recommend Hanoi over Saigon. Much more interesting place to see, definitely more influenced by the Chinese and less Western (Saigon is a large, western-style city in many ways). There's also a bit of gay life in Hanoi.
From there I would explore either northern or central Vietnam. Hoi An is a good recommendation. The overnight train from Hanoi is a more pleasant experience that you might imagine, although not luxury!
Where are you flying in from/connecting via? If you're seeking more of a gay scene during your stay then connecting via Bangkok and spending a couple of nights there will definitely deliver on that.
But definitely see Vietnam... good choice.