Well - unlike the Spinosaurus - T.rex comparison, the Giganotosaurus - T.rex comparison is much closer, at least among the real life versions.
Based on their skeletons - Spinosaurus is estimated to be about to be roughly 2-3 meters longer than T. rex, and about 2-3 tons heavier than T.rex.
By comparison - the holotype for Giganotosaurus is roughly the same length as Sue the T.rex(about 12.3-12.5 meters). The largest Giganotosaurus is estimated to be only about 70-90 cm longer than Sue. However - T.rex is slightly taller and slightly more massive. Sue is about 4 meters tall at the hips, while Giganotosaurus is about 3.8 meters at the hip. Sue is estimated to have weighed about 8.4 metric tons, while the largest Giganotosaurus specimen is estimated at 8.2 metric tons.
As I have already stated(in the Spinosaurus debate) - when we look at the T.rexes from the JP/JW series - things get blurred even more. As the largest T.rex in the series - is Rexy from Jurassic World - at about 13.4 meters/44 feet long, 5.1 meters/16.8 feet tall, and may have weighed about 9 metric tons. She would actually be slightly longer than the largest Giganotosaurus.
And they found a skull 20 cm larger than that too, hitting 1.8 meters in length. Which is evidence enough of a larger skull than t-rex, correct?
While The 1.8 meter long skull for Giganotosaurus is an over-exaggeration. When corrected - the holotype Giganotosaurus skull is about 1.57 meters. While the largest specimen is estimated at about 1.65 meters. By comparison - the largest skull for T.rex is about 1.5 meters. So yes - the Giganotosaurus skull is slightly longer.