The similarity between Elijah and John the Baptists is understood the same way by most Protestant Commentaries including John Wesley’s.
This is understood to mean:
With the same integrity, courage, austerity, and fervour, and the same power attending his word (John Wesley's Notes, Luke 1:17)
However to understand this brief comment by Wesley one really has to appreciate the history of Elijah to see how truly John the Baptist was almost exactly like him. The problem is simply that nowadays people are not that familiar with Old Testament figures and how the fit it into salvation history.
Anyone, after reading the history of Elijah in the Old Testament setting would probably make these sorts of observations.
He was a large looming figure, surpassing the greatness of most prophets, if not all. He was almost along the lines of Moses, which makes his appearance with Moses at the Mount of Transfiguration not so surprising as. Elijah’s greatness is probably due to the impression that the world and especially the apostasy of Israel had reached its lowest point. Prophets were essentially defenders of Jehovah and of the Laws of Moses. Elijah, ‘suddenly’ appeared on this deplorable state of the world, desperately needing reform, with a ‘ferocity’ and ‘stern ruggedness’ that leaps out of the scriptures in fiery, rebukes, challenges and contests. He essentially stands alone saying ‘Repent!’ to Israel with unmoving faithfulness and unflinching fearlessness, like a man with a face of flint.
This unbending, unfaltering spirit of sternness and severity, like a man cracking the whip of God, was predicted to come again to usher in Messiah’s entrance into the world. This expectation was a central one in the Jew’s mindset about the coming kingdom. For details refer here: What kind of Elijah did the Jews expect.
Even his and the Baptists appearance ‘with an upper garment of black camel’s hair with a leather belt’ (2 Kings 1:8) so aptly represented their spirit:
John had his raiment of camels' hair - Coarse and rough, suiting his character and doctrine. (John Wesley's Notes, Mathew 3:4)
I think it is under this perspective that miracles play no part in the idea of ‘spirit and power’, for although miracles are powerful to persuade people that God is speaking it is really the words and message that these men had to Israel, which reflects all the power they had in their spirit. Furthermore as the Baptist's mission was meant 'to decrease' while Christ’s 'increased', miracles would have not served the spirit of his mission. His main duty was to call every Jew to a Baptism of repentance in preparation of Christ ‘whose sandals he was not worthy to untie'. Just as Elijah called Israel back to Jehovah as a lost people under God’s anger, so the Baptist called the Jews to be baptized like Gentile converts, fully emerging into a new life of reformed expectation for a great salvation.
It is all these ideas that bring Wesley to make his brief notes on the subject as he does.
