The answer to the question of whether a 6.0 engine is compatible with a 5.3 transmission is no. The 6.0 engine is significantly larger and heavier than the 5.3 engine, and the two are incompatible. The 6.0 is also far more potent than the 5.3.
However, it is possible to replace the 5.3 transmission with one that is compatible with the 6.0 if you have the necessary components and equipment. However, this can be a costly and time-consuming process, and it may be more efficient to simply upgrade to a 6.0-liter engine.
The author of the above FACT has learned this lesson the hard way. After installing the 8.1/Allison in his 2005 2500 HD, he acquired 50 more horsepower and 120 lb-ft of torque, a 14-bolt rear, 4.10s, a transmission seen in medium-duty diesels and fire trucks, four-wheel disc brakes, and a driveshaft the size of his thigh. In retrospect, he wishes he had replaced his 5.3 transmission with a 6.0 transmission much earlier.
Therefore, if you’re seeking to upgrade your engine and transmission, the 6.0 is the best alternative; the 5.3 transmission will not fit.