How would win in a battle between a Giant Tiranosaurius Rex and Godzilla?
Godzilla. Canonically Godzilla's atomic breath is capable of killing most kaiju (giant monsters) in one hit. Assuming the T-Rex is about the same size as Godzilla, it would only have its bite and tail to attack Godzilla with. His hide is known to be more or less immune to e.g. tank shells, so it is unlikely that the T-Rex's teeth would be able to damage him. Ultimately, Godzilla would probably destroy the T-Rex quite quickly.
What if the T-Rex was twice as big as Godzilla?
A regular sized T-Rex was up to 40 feet long and 12 feet high, weighing between 5,000 and 7,000 kilograms. Godzilla canonically is 394 feet (120 meters) tall. T-Rex being twice as high as Godzilla would would be 66 times its original hight. Mass of the object scales cubically, with object's  length. This means that T-Rex would weigh nearly 2 million tonnes. The biggest know living animal ever lived is a blue whale weighing up to 180 tonnes. Clearly, T-Rex, being this big, would suffer from a heart failure, wouldn't be able to support his weight and would probably overheat making him unable to fight Godzilla. Hence Godzilla would win by walkover.