This is a trick question, since it's not really either/or. Part of spreading the kingdom is preaching the Gospel (with words, Francis). The other part is stuff like physical healing, mental healing, and social healing. Oh, and exorcisms.
But I maintain that the Spiritual aspect of spreading the kingdom is more important than the physical aspect. In John 6, Jesus miraculously fed about 20,000 people, in a physical act of the Kingdom of God breaking into this world. However, the very next day, he said stuff like the following (vv. 26-29):
"Jesus answered, 'I tell you the truth, you are looking for me, not because you saw miraculous signs but because you ate the loaves and had your fill. Do not work for food that spoils, but for food that endures to eternal life, which the Son of Man will give you. On him God the Father has placed his seal of approval.' Then they asked him, 'What must we do to do the works God requires?' Jesus answered, 'The work of God is this: to believe in the one he has sent.'And then during the rest of the often spiky interchange between Jesus and the people, narrated in chapter 6, Jesus continued to drive home how much more important the spiritual aspect is than the physical. "The flesh profits nothing."
Here's another thing: the people had all benefited from a tremendous miracle, and the very next day they asked Jesus for a sign! What gall! A wise man, Jay Carty, once preached that miracles are like Chinese food. You're hungry two hours later.
Here's a disclaimer: I'm big on physical outworkings of the power of God. I'm a member of a Vineyard Church, and one of my biggest peeves is Cessationism. What an abomination!
It's not: 100% effort to one and 0% to the other. I don't know if I'd even put percentages on it, because the two are inextricably linked.