"9And it came to pass, when they were gone over, that Elijah said unto Elisha, Ask what I shall do for thee, before I be taken away from thee. And Elisha said, I pray thee, let a double portion of thy spirit be upon me. 10And he said, Thou hast asked a hard thing: nevertheless, if thou see me when I am taken from thee, it shall be so unto thee; but if not, it shall not be so." (2 Kings 2: 9-10)
Elijah is a picture of the Old Covenant, in which man knew that "God is", and His presence and manifestation was nothing but judgment.
Elisha, whose name means "God saves" is a picture of Jesus, Grace and Truth personified, who enacted the New Covenant of God's grace in our lives.
Consider how Elijah just spoke to bring drought to Israel:
"And Elijah the Tishbite, who was of the inhabitants of Gilead, said unto Ahab, As the LORD God of Israel liveth, before whom I stand, there shall not be dew nor rain these years, but according to my word." (1 Kings 17: 1)
He just spoke, and by God's authority in him, there was no rain.
When it came to bringing rain, though, Elijah struggled:
"1And it came to pass after many days, that the word of the LORD came to Elijah in the third year, saying, Go, shew thyself unto Ahab; and I will send rain upon the earth. 2And Elijah went to shew himself unto Ahab. And there was a sore famine in Samaria." (1 Kings 18: 1-2)
Notice the severity of the famine.
"41And Elijah said unto Ahab, Get thee up, eat and drink; for there is a sound of abundance of rain. 42So Ahab went up to eat and to drink. And Elijah went up to the top of Carmel; and he cast himself down upon the earth, and put his face between his knees, 43And said to his servant, Go up now, look toward the sea. And he went up, and looked, and said, There is nothing. And he said, Go again seven times" (1 Kings 18: 4-1-43)
Notice that when praying for rain, not judgment but blessing, Elijah struggled. He had an Old Covenant mentality, one which curses us when we fail.
When Jezebel threatened to kill Elijah, he fled, because the Old Covenant does not accord us boldness. When God gave Elijah three commandments, he only fulfilled one of them: anointing his successor.
As for Elisha, he went about healing and doing good, just like Jesus! (Acts 10: 38)
When Elijah called for fire to burn up his adversaries, Elisha struck them with blindness, led them captive to the king of Israel, who gave them bread, then sent them home.
Elijah killed (1 Kings 18:40). Elisha healed and restored life (2 Kings 6), even after his death (2 Kings 13: 21).
In every way, through the grace of God, Elisha's ministry surpassed Elijah's, and Jesus's ministry today, the New Covenant of grace, surpasses the Old Covenant of law.