What was the difference between Jesus walking here as a man of flesh and the first Adam before he disobeyed God?
Adam was tempted and succumbed to it sinning.
Jesus was tempted but never yielded to the temptations. Could he have? I do really believe so. Adam was clean and Jesus was clean at their beginning of their respective times as men of flesh. Adam dirtied himself. Jesus overcame the desires to dirty himself. The last battle against the temptations in his flesh were, as I see it, won in the Garden of Gethsemane, here:
"And he went a little farther, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as thou wilt." Matt 26:39
After that he still needed to go to the cross and die, but his own flesh and the ways of his flesh had been completely defeated. No more temptations for Jesus! He had overcome the world of temptation in the son of man, Jesus.
First see the confirmation by Jesus here:
"These things I have spoken unto you, that in me ye might have peace. In the world ye shall have tribulation: but be of good cheer; I have overcome the world." John 16:33
Jesus did not overcome planet Earth nor did he overcome the worlds for each of us, but he was readying himself in order to open up the Way and to provide access to the power that each us could do what he did.
And then the clarification here:
"And now I am no more in the world, but these are in the world,..." John 17:11
Jesus was still on planet Earth and still had to go to the cross to die, but he was no longer in the world of those temptations, which when followed lead people to sin. John describes them here:
"For all that is in the world, the lust of the flesh, and the lust of the eyes, and the pride of life, is not of the Father, but is of the world.
And the world passeth away, and the lust thereof: but he that doeth the will of God abideth for ever." I John 2:16-17
For Jesus the "world" of temptations was gone. We, however, as per John 17:11 are, each one us, still in our own little world of temptations until and if we have by the power of the Holy Spirit in us overcome as Jesus did! Who at this moment is like with Jesus no longer in that "world"?
Is it impossible for the Holy Spirit in us to overcome that world before the dirt is thrown over our faces? Jesus did it before he died physically. What kind of a limit should we put on the power of God?