Jesus is a much better big brother than Esau. Both were willing to give something up, but one gave up to his shame, the other to His glory.
Esau despised his birthright. He was born into a special position but it meant nothing to him, so he basically gave it to his brother. Jesus is the firstborn of creation and the firstborn from the dead. He did give up glory, in a way for a time (see Philippians 2:5-11), but not because He despised His position. Instead it was so that He could eventually share more glory with His brothers.
Therefore he had to be made like his brothers in every respect, so that he might become a merciful and faithful high priest in the service of God, to make propitiation for the sins of the people. (Hebrews 2:17)
Even though Jesus had and has a unique place in the heavenly Father’s heart, Jesus did not rub that in. He doesn’t flaunt His exalted position or work to make us feel that we don’t have it. He identified with us, He was “made like his brothers,” in order to “make propitiation,” meaning that our older Brother won His Father’s favor for us by dying for our sins.
At our remembrance of Him in communion He brings us closer to the Father and to each other. He overcomes our grasping for preeminence, our tantrums and envy and posturing. He feeds us. He Himself is our food and our drink by faith. Our Brother did not despise His birthright, but despised the shame of the cross and is the founder and perfector of our faith.