This is an important question.
Luckily, the gospels and Ash-Shifa can answer it for us. (Ash-Shifa is a 12th century biography of Muhammad that is considered authoritative throughout the Muslim world.)
Let's take Jesus' spit first.
- In Mark's gospel, Jesus cured a deaf man by putting some of his holy spit on the deaf man's tongue.
And they bring unto him one that was deaf, and had an impediment in his speech ... And he ... put his fingers into his ears, and he spit, and touched his tongue ... And straightway his ears were opened, and the string of his tongue was loosed, and he spake plain. Mark 7:32-35
- And he cured a blind man by spitting on (or in) his eyes.
And they bring a blind man unto him ... And ... he ... spit on his eyes [and] asked him if he saw ought. And he looked up, and said, I see men as trees, walking. After that he put his hands again upon his eyes, and made him look up: and he was restored, and saw every man clearly. Mark 8:22-25
- The only other gospel that mentions Jesus' spit is John, which says that another blind man (or was it the same one?) was cured with mud made with Jesus spit followed by a holy water bath.
And as Jesus passed by, he saw a man which was blind from his birth. And his disciples asked him, saying, Master, who did sin, this man, or his parents, that he was born blind? Jesus answered, Neither hath this man sinned, nor his parents: but that the works of God should be made manifest in him .... When he had thus spoken, he spat on the ground, and made clay of the spittle, and he anointed the eyes of the blind man with the clay, And said unto him, Go, wash in the pool of Siloam ... He ... washed, and came seeing. John 9:1-7
(All quotes are taken from Ash-Shifa.)
- Just like Jesus, Muhammad cured blind and deaf people by spitting in their eyes or ears.
Habib, either the son of Fudayk or Furayk's said that his father's eyes became so white that he had no vision at all. The Messenger of Allah, praise and peace be upon him, blew some of his saliva in to his eyes whereupon his vision was immediately restored. He was even seen threading a needle at the age of eighty! (p. 188)
At the Battle of Khybar, Ali's eyes became very painful. The Prophet, praise and peace be upon him, blew some of his saliva on them and they were immediately healed. (p. 188)
A lady from Khuth'am had a child who was mute. The Prophet, praise and peace be upon him, asked for some water to be brought with which he rinsed his mouth and washed hands. Then he gave it to the mother and told her to wash the child and wipe him with it. The mother did as the Prophet, praise and peace be upon him, had said and the child was no longer mute and had an intellect superior to most people. (p. 189)
- And like Moses, he could make water miraculously appear. But he didn't have to strike a rock with his rod or even speak to the rock. He did it all with his spit.
At Hudaybiyah, we are told by Al Bara', there were approximately 14,000 men, and the water well they found was insufficient to provide for even fifty sheep. The Companions crowded around the well until not one single drop remained. Then, the Messenger of Allah, praise and peace be upon him, came and sat beside it and a pail was brought to him in which he blew some of his saliva and supplicated. Salama reported that he either supplicated or blew some of his salvia in it whereupon water gushed forth and there was sufficient water for themselves and enough to fill their containers. (p. 170)
- Like Jesus, Muhammad cured people with mud made with his own spit. But Muhammad's muddy spit treatment was administered orally rather than topically.
Mula'ib's son suffered from an edema of water fluid, and sent a messenger to the Prophet, praise and peace be upon him, to tell him of his condition. The Prophet, praise and peace be upon him, took some dust from the ground, blew some of his salvia upon it and gave to the Mula'ib's messenger who was amazed and took it fearing that he would be laughed at. He returned to Mulai'b's son who was now on the verge of death and gave it to him. He consumed it and Allah cured him.
- And Muhammad's spit, unlike Jesus', cured more than just blind and deaf people. It also worked on burn and hernia patients.
There was a lady who brought her possessed son to the Prophet, praise and peace be upon, and Abbas' son tells us that the Prophet, praise and peace be upon him, stroked his chest whereupon the child vomited something that resembled a black puppy and was immediately cured. We are also told of the time Muhammad, Hatim's son was a child and a boiling pot overturned on his arm, the Prophet, praise and peace be upon him, stroked it, supplicated, then blew some of his salvia on it and it was immediately healed. (p. 189)
A man came to him suffering from a hernia. He instructed that it be sprinkled with water from a spring into which he had blown some saliva. After this had been carried out the man was cured. (p. 196)
- Bad mannered girls behave much better after eating food from Muhammad's mouth. (There's nothing like this in the gospels.)
A girl who was in the service of the Prophet, praise and peace be upon him, asked him for some food when he was eating and as he never refused anyone anything he gave her what was in front of him. The girl was persistent and said, "I want the food in your mouth." So he gave her what was in his mouth. After she had swallowed it, she became well mannered and the change was apparent for all to see, and she became among the most well mannered girls of Medina. (p. 189)
- Many soldiers were completely healed by rubbing Muhammad spit on their wounds. (Something similar occurred during Jesus' arrest, when a man with a severed ear was restored by Jesus' touch. But since no spit was involved, it doesn't count in the holy spit competition.)
Abu Sa'id Al Khudri said that the Prophet, praise and peace, be upon him, put some of his saliva on the mark made by the arrow on the Day of Dhu Qarad and Abu Katada told him that it neither throbbed nor yet became infected. (p. 187)
During the Battle of Uhud, Kulthum Hussain's son was shot in his throat. The Messenger of Allah, praise and peace be upon him, blew some of his saliva upon it and it healed immediately. Abdullah, Anies' son was also among those injured during the encounter and sustained a wound to his head, once again the Prophet, praise and peace be upon him, blew some of his saliva upon it and it did not turn septic. (p. 188)
Salama, Al Akwa's son sustained a wound to his thigh during the battle and a similar miracle occurred whereby he too was immediately healed. (p. 188)
- And finally, and most impressively, Muhammad cured amputees with his spit. (Not even God can do that!)
It was during the Battle of Badr that Abu Jahl severed the hand of Mu'awwidh, Afra's son. Mu'awwidh went to the Prophet, praise and peace be upon him carrying his severed hand, whereupon the Prophet, praise and peace be upon him, blew some of his saliva on it, replaced it was immediately miraculously rejoined to his arm. It was during the same battle Wahb's son tells us that Khubaby, Yasaf's son was severely struck on the neck and half of it was severed. The Messenger of Allah, praise and peace be upon him, blew his salvia upon it and it was immediately healed. (p. 188-9)
So Muhammad wins the holy spit contest. I guess we should all convert to Islam. (What more evidence could anyone ever ask for?)