I wouldn’t trust any kind of concrete speed estimate to be honest. However, "6 mph" is too low.
Osteological evidence clearly suggests giant theropods, especially Tyrannosaurids, had more cursorial adaptations than similar-sized elephants (non-columnar limbs with digitigrady and flexed posture, larger limb muscles), and elephants can at least approach, if not exceed, 20 km/h, which suggests that giant theropods must have been capable of at least that.
The open question is, how much more? And whether their more cursorial limb proportions translated into superior athletic potential such as the ability to run properly, with an airborne phase, or whether they were just there to enhance safety factors or efficiency.
In direct comparison with Giganotosaurus, Tyrannosaurus has the more cursorial limb proportions and larger (proximal) limb muscles, suggesting that it was likely faster and more efficient at top speed. However the differences are likely not exactly huge.
There is some evidence that suggests giant carcharodontosaurs may have been more geared towards stability (dorsally located femoral head allowing a wider stance/more lateral abduction of the hindlimb, and lighter skull and head making the animal less top-heavy) rather than speed and agility.
Seeing how Giganotosaurus was probably typically heavier than T. rex, T. rex being "heavy" ceases to be an argument one way or another.