What is the difference between the bodies of Krishna and humans?

The difference is that for us, the body and soul are different.  For Krishna, there is no difference between His body and soul.

SRILA PRABHUPADA SAYS:

“When the Isopanisad describes the Supreme Lord as "He who is the greatest of  all, who is embodied and omniscient," this shows the distinction between God and ourselves. 

We are embodied. Therefore my body is different from me. When “I” leave this body, it becomes dust. 

As the Bible says, "Dust thou art, and unto dust shalt thou return." But I am not dust; I am a spirit soul. Therefore thou means "the body." 

Krsna, however, is not embodied. This means there is no difference between His body and His soul. 

In other words, His body is pure spirit. Therefore He does not change His body. And because He does not change His body, He is omniscient--He remembers everything. 

Because we do change our material bodies, however, we forget what happened in our last birth. We have forgotten who we were, just as when we sleep we forget our body and our surroundings. The body becomes tired and rests; it becomes inactive. 

In contrast, in a dreamland I work, I go somewhere, I fly, I create another body, another environment. This we experience every night. It is not difficult to understand”.