Wouldn't the difference be in CV conditioning? If the HR is going up pushing weight in response to forcing blood through contracting muscle, and in response to adrenaline it's one thing. However, if HR goes up moving a high volume of blood to keep muscles in motion, processing large quantifies of O2, improving efficency of the oxidative system, it's another.
I agree that circuit has elements of both, but not complete training in either.
I've done it for about a year, and like it, and will probably go back to it.
However I am trying the traditional aerobic combined with weights for now.
Sometimes you feel you have to mix up the mixed up by unmixing it