It’s both really but for me it will always fundamentally be about the drivers.
I make a distinction between the team effort and the constructor themselves. Just as it’s not just the driver who builds the car, plans the strategy, etc. the driver himself does more than get in the car and drive it. That’s why it’s a team effort; but I see it as a team effort in the sense of it being the product of many people, rather than as a sport which is competed on a team (i.e. the constructor) basis. After all, the WDC is the older, more prestigious championship and constructors’ points are just the two drivers’ points added together, rather than simply their best result (an idea I explored here)
To me it’s only a constructor victory if we see a 1-2 in a race or the championship, or the constructor takes both championships. Other than those, for me it’s the driver’s victory, but of course it’s really the driver’s team (i.e. his side of the garage plus of course some credit to the general management) victory. So for example last year Red Bull won the championship, but if they hadn’t it would have been Alonso, not Ferrari.
A weird and probably not entirely logical way of looking at things, but that’s my view.