Why did he suffer "under Pontius Pilate, as judge"?
That he, being innocent, and yet condemned by a temporal judge,1 might thereby free us from the severe judgement of God to which we were exposed.2
Is there anything more in his being "crucified", than if he had died some other death?
Yes there is; for thereby I am assured, that he took on him the curse which lay upon me;3 for the death of the cross was accursed of God.4
1 John 18:38; Matt. 27:24; Acts 4:27 , 28; Luke 23:14, 15; John 19:4.